To identify the missing number in the series 23 5 7 11 17, we need to find out the pattern or the logic being followed in the series. From the given series, we can see that the first number is a prime number, and each subsequent number is the sum of the two preceding prime numbers.

So, 5 is the sum of the first two prime numbers, 2 and 3. Similarly, 7 is the sum of 3 and 4, 11 is the sum of 4 and 7, and 17 is the sum of 7 and 10. Therefore, to find the missing number, we need to figure out the next prime numbers after 10 and 7 and their sum.

The next prime number after 10 is 11, and the next after 7 is 11 as well. Therefore, to continue the sequence, we simply need to add 11 and 11, which results in 22.

Hence, the missing number in the given series is 22.

## Which number should come next in the series 1 2 3 5 7 11?

The given series of numbers, namely 1 2 3 5 7 11, appears to be a sequence of prime numbers. Prime numbers are those numbers that can only be divided evenly by 1 and themselves. It is evident from the series that each number after 3 is obtained by adding the previous two numbers.

Therefore, to determine the next number in the sequence, we need to add the last two numbers in the series, which are 7 and 11 respectively.

The sum of 7 and 11 is 18. However, it’s not enough to say that 18 is the next number. We need to check whether it is also a prime number or not.

Upon further examination, we find that the number 18 is NOT a prime number as it can be evenly divided by 2, 3, 6, and 9. Therefore, it cannot be the next number in the series of prime numbers.

The next prime number after 11 is 13. Moreover, we can also confirm this by examining whether 13 follows the same pattern as the other numbers in the series.

When we add 7 and 11, we get 18. If we add 11 and 13, we get 24. This indicates that 13 is the next term in this series of prime numbers.

Therefore, the next number in the series 1 2 3 5 7 11 is 13.

## Which number replaces the question mark for the following numbers 2 3 5 7 11 13 17 19?

The given sequence of numbers appears to be the first eight prime numbers starting from 2, which are: 2, 3, 5, 7, 11, 13, 17, and 19. Prime numbers are those natural numbers greater than one that cannot be expressed as the product of two smaller natural numbers, and they have a special property that makes them distinct from other numbers.

Every prime number, except for 2, is an odd number. Moreover, two consecutive odd numbers have an even number between them that is divisible by 2, which means that every prime number, except for 2, is followed by an even number, which is not a prime.

Therefore, the next number in this sequence that follows the last prime number 19 is an even number, which is not a prime. The next even number after 19 is 20 because it can be divided by 2 without a remainder. However, 20 is not a prime number because it can be expressed as the product of two smaller natural numbers, namely 2 and 10, or 4 and 5, or 1 and 20.

Therefore, 20 cannot replace the question mark in the given sequence of prime numbers.

Similarly, any other even number greater than 19 cannot be a candidate for the missing number in this sequence because it is not a prime number. Moreover, any odd number greater than 19 cannot be a candidate for the missing number either because, by definition, it cannot be a prime number if it is not divisible by any of the previous prime numbers in this sequence.

Therefore, the only possible number that can replace the question mark in the given sequence of prime numbers is the next prime number after 19. To determine this number, we can use different methods, such as trial division, sieve of Eratosthenes, or generating functions.

One method is to use trial division, which involves dividing a natural number by all possible smaller natural numbers up to its square root to see if it is divisible by any of them. For example, to test if 21 is a prime number, we divide it by all possible smaller natural numbers up to its square root, which is about 4.58 (rounded up to 5), as follows:

21 ÷ 2 = 10.5 (not an integer)

21 ÷ 3 = 7 (an integer, but not a factor)

21 ÷ 4 = 5.25 (not an integer)

21 ÷ 5 = 4.2 (not an integer)

Since 21 is not divisible by any of the previous prime numbers in this sequence, it might be a prime number. To confirm this, we can divide it by the next prime number after 5, which is 7, as follows:

21 ÷ 7 = 3 (an integer)

Since 21 is divisible by 7, it is not a prime number, but a composite number that can be expressed as the product of two smaller natural numbers, namely 3 and 7. Therefore, 21 cannot replace the question mark in the given sequence of prime numbers.

Using this method, we can continue testing all natural numbers greater than 19 until we find the next prime number after 19, which is 23. To test if 23 is a prime number, we can divide it by all possible smaller natural numbers up to its square root, which is about 4.8 (rounded up to 5), as follows:

23 ÷ 2 = 11.5 (not an integer)

23 ÷ 3 = 7.67 (not an integer)

23 ÷ 4 = 5.75 (not an integer)

23 ÷ 5 = 4.6 (not an integer)

Since 23 is not divisible by any of the previous prime numbers in this sequence, it might be a prime number. To confirm this, we can divide it by the next prime number after 5, which is 7, as follows:

23 ÷ 7 = 3.29 (not an integer)

Since 23 is not divisible by 7 or any other natural number up to its square root, it is a prime number that follows 19 in the sequence of prime numbers. Therefore, the number that replaces the question mark in the given sequence is 23.

## How do I find a missing number?

Finding a missing number can be a tricky task, but there are several methods that can help you determine the missing value. Firstly, you need to determine the pattern or sequence that the numbers follow. This could be arithmetic, geometric, or some other type of pattern. Once you have identified the pattern, you can use it to determine the missing number.

One common method to find the missing number in an arithmetic sequence is to use the formula for the nth term of the sequence. The formula is given by Tn = a + (n-1)d, where Tn is the nth term, ‘a’ is the first term, ‘n’ is the number of terms, and ‘d’ is the common difference between the terms. If you know any three values of the sequence, you can easily calculate the fourth value, which would be the missing number.

For example, suppose you have the sequence 2, 4, 6, _, 10. Here, ‘a’ = 2, ‘d’ = 2, and ‘n’ = 5. Using the formula T5 = a + (n-1)d, we get T5 = 2 + 4 = 6. Therefore, the missing number in the sequence is 6.

Another way to find the missing number is to use the sum of the series formula. If you know the sum of the sequence and all the other values except for one, you can use this formula to calculate the missing number. For example, if the sequence is 4, 8, 12, 16, _, and the sum of the sequence is 60, you can use the formula ‘Sn = [n/2] x [2a + (n-1)d]’ to find the missing number.

Here, n = 5, ‘a’ = 4, ‘d’ = 4, and ‘Sn’ = 60. By substituting these values, we get 60 = [5/2] x [2(4) + (5-1)(4)], which gives us the missing number as 20.

Finding a missing number requires you to understand the sequence pattern and use appropriate methods to calculate the missing value. Using formulas such as the nth term or the sum of the series formula can help you determine the missing number efficiently. However, it is important to keep in mind that there may be more than one possible answer, and it is crucial to double-check your calculations to ensure accuracy.

## How do you solve a number puzzle?

Number puzzles come in various forms, and the strategies used to solve them may differ. However, some general techniques can be applied to most number puzzles to arrive at solutions. Here are some steps that can help solve a number puzzle:

1. Understand the rules: Before attempting to solve a number puzzle, the first and crucial step is to understand its rules. Knowing the rules helps in identifying patterns, recognizing clues, and deducing possible solutions. Some number puzzles are based on math concepts, while others require logical reasoning or observation.

2. Identify the patterns: Once you know the rules, look for patterns in the puzzle. In some number puzzles, the solution follows a pattern, such as a sequence of multiples, Fibonacci series, or geometric progression. Identify the pattern and try to apply it to the rest of the puzzle.

3. Trial and error: Trial and error is a way to solve some number puzzles. Start with one possible solution and use logic to work through the rest of the puzzle. If that choice fails, try another solution and keep going until a pattern or logic emerges.

4. Elimination: In some number puzzles, you can eliminate possible solutions using logic. For example, if a puzzle requires nine numbers in a 3×3 grid, and you already know seven, you can deduce which of the two remaining numbers fits in which spot.

5. Cross-referencing: In some number puzzles, one part of the puzzle can help in solving another part. Cross-reference clues or bits of information to derive a solution.

6. Visualization: Visualize the puzzle, especially when it is a three-dimensional puzzle. For example, when attempting a Rubik’s Cube, visualize the cube before making any moves, and work backward from what you want to achieve.

7. Time management: Finally, number puzzles can be time-consuming, and sometimes the solutions can elude us. Try not to get stuck on one puzzle for too long; come back later with fresh eyes or take a break.

The key to solving a number puzzle is to understand its rules, identify patterns, use logic and intuition, and remain patient and persistent. With practice, you can develop the strategic thinking and problem-solving skills to solve even the most complex number puzzle.

## How do you find the missing number in a number sentence?

There are various methods you can use to find the missing number in a number sentence. One approach is to use inverse operations. In a typical number sentence, you have two numbers with an operator in between them. For example, 5 + __ = 9. To find the missing number, you need to know what operation was used and its inverse operation.

In this instance, the operation used was addition, and the inverse operation is subtraction.

To find the missing number, you can subtract the known value from the result. In the above example, you subtract 5 from 9 to get the missing number which is 4. Alternatively, you can subtract the missing number from the result to get the known value. Hence, the equation can be rewritten as 9 – __ = 5, and the missing value is 4 once again.

Another method is to use patterns and algebraic equations. Given two values, there may be a pattern that exists between them, such as sequence, ratio, or proportion. If the pattern is known, it’s possible to determine the missing value. For instance, if given the numbers 2, 4, __, 8, you may notice that the pattern is a sequence where each number is double the previous one.

Accordingly, the missing number would be 4 x 2 = 8.

Algebraic equations can also be used to solve missing number problems. In this case, you represent the unknown variable using a letter, say x, and use equations to solve for x. For example, if given the number sentence 3x + 7 = 22, you can isolate x by subtracting 7 from both sides to get 3x = 15, then divide by 3, hence x = 5.

Finding a missing number in a number sentence requires identifying the operation being used, recognizing any patterns or sequences, and solving an algebraic equation if necessary. With these methods, you can easily find the missing number in any number sentence posed to you.

## What pattern is used to write the sequence 3 5 7 9 11 13?

The pattern used to write the sequence 3 5 7 9 11 13 is an arithmetic sequence. An arithmetic sequence is a sequence where the difference between consecutive terms is a constant. In this case, the difference between consecutive terms is 2. Therefore, the formula for the nth term of this arithmetic sequence can be written as:

an = a1 + (n-1)d

where an denotes the nth term, a1 denotes the first term, and d denotes the common difference. In this sequence, a1 is 3 and d is 2. Substituting these values into the formula gives:

an = 3 + (n-1)2

Simplifying this expression further gives:

an = 2n + 1

Therefore, the nth term of this sequence can be found by adding 1 to twice the value of n. For example, the 4th term of this sequence can be found by plugging in n = 4 into the formula to get:

a4 = 2(4) + 1 = 9

So, the 4th term of the sequence is 9. Thus, this arithmetic sequence has a constant common difference of 2, which is why each term can be obtained by adding 2 to the preceding term.

## What is the sum of the arithmetic sequence 5 7 9 11 23 59 40 25 140?

To find the sum of an arithmetic sequence, we need to know the formula for the sum of n terms of an arithmetic sequence. This formula is:

Sn = n/2[2a + (n-1)d]

where Sn is the sum of n terms, a is the first term of the sequence, d is the common difference between consecutive terms, and n is the number of terms in the sequence.

In this case, we have the arithmetic sequence 5 7 9 11 23 59 40 25 140, with a = 5 and d = 2 (since the sequence increases by 2 each time). We can count the number of terms in the sequence to get n = 9.

Plugging these values into the formula, we get:

Sn = 9/2[2(5) + (9-1)2]

Sn = 9/2[10 + 16]

Sn = 9/2[26]

Sn = 9(13)

Sn = 117

Therefore, the sum of the arithmetic sequence 5 7 9 11 23 59 40 25 140 is 117.