Question

Use inductive reasoning to predict the next number in each of the following list.

2, 5, 10, 17, 26, ?

Answer 1

Solution

The logic behind the terms of the given series is simple, the first term is 2 and the second term is 5

$2 + 3 = 5$

The third term is 10

$5 + 5 = 10$

The fourth term is 17

$10 + 7 = 17$

The fifth term is 26

$17 + 9 = 26$

Hence, we are adding consecutive odd numbers starting from 3 to each preceding term.

The next number to be added to 26 will be 11

$26 + 11 = 37$

The next two consecutive odd numbers after 11 is 13 and 15 .Thus, the next 2 numbers in the series will be:

$37 + 13 = 50$

$50 + 15 = 65$

Thus, the next three terms in 2, 5, 10, 17, 26 ... are 37, 50, and 65.