Reasoning — Number Series

The pattern in the series is adding 7 to the previous number. 12 + 7 = 19 19 + 7 = 26 26 + 7 = 33 Following this pattern, the next number will be 33 + 7 = 40.

The pattern in the series is multiplying the previous number by 3. 3 * 3 = 9 9 * 3 = 27 27 * 3 = 81 Following this pattern, the next number will be 81 * 3 = 243.

Let's find the differences between consecutive terms: 12 - 5 = 7 26 - 12 = 14 54 - 26 = 28 The differences are 7, 14, 28. This is a geometric progression where each difference is multiplied by 2. So, the next difference will be 28 * 2 = 56. Adding this to the last term: 54 + 56 = 110.

The pattern in the series is the cube of consecutive natural numbers. 1 = 1^3 8 = 2^3 27 = 3^3 64 = 4^3 Following this pattern, the next number will be 5^3 = 125.

The pattern in the series is (previous number * 2) + an increasing natural number starting from 1. 4 * 2 + 1 = 9 9 * 2 + 2 = 20 20 * 2 + 3 = 43 Following this pattern, the next number will be 43 * 2 + 4 = 86 + 4 = 90.

Let's find the differences between consecutive terms (First difference): 10 - 7 = 3 16 - 10 = 6 28 - 16 = 12 The first differences are 3, 6, 12. Now, let's find the differences between these first differences (Second difference): 6 - 3 = 3 12 - 6 = 6 The second differences are 3, 6. This indicates a pattern of multiplying by 2. So, the next second difference will be 6 * 2 = 12. The next first difference will be 12 + 12 = 24. Adding this to the last term: 28 + 24 = 52.

The pattern in the series is n^2 + 1, where n is the position of the term starting from 1. 1^2 + 1 = 1 + 1 = 2 2^2 + 1 = 4 + 1 = 5 3^2 + 1 = 9 + 1 = 10 4^2 + 1 = 16 + 1 = 17 5^2 + 1 = 25 + 1 = 26 Following this pattern, the next number (6th term) will be 6^2 + 1 = 36 + 1 = 37.

The series consists of prime numbers in ascending order. 2, 3, 5, 7, 11 are the first five prime numbers. The next prime number after 11 is 13.

This is a Fibonacci series, where each number is the sum of the two preceding ones. 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 Following this pattern, the next number will be 5 + 8 = 13.

Let's find the differences between consecutive terms: 99 - 100 = -1 95 - 99 = -4 86 - 95 = -9 70 - 86 = -16 The differences are -1, -4, -9, -16. These are the negative squares of consecutive natural numbers: -1 = -(1^2) -4 = -(2^2) -9 = -(3^2) -16 = -(4^2) Following this pattern, the next difference will be -(5^2) = -25. Subtracting this from the last term: 70 - 25 = 45.