Question

How do you find the next three terms in 2, 5, 10, 17, 26 . . . .?

Answer 1

Hint: This is a logical question and we need to use our logical reasoning to solve this question. The logic behind this question is that each term of this sequence is obtained by increasing with consecutive odd numbers. Using this logic, we can find the next three terms.

Complete step-by-step answer:
In this question, we are given a sequence and we have to find the next three terms of this sequence.
Given sequence: 2, 5, 10, 17, 26 . . .
A sequence is an arrangement of some elements in a particular order.
Now, this is a logical question and there can be many logics that we can use to solve this question and since there are no options given there can be multiple correct answers to this question.
Let us find the logic behind this sequence and find its next three terms.
Here, first term is 2.
Next term is 5 which is 3 more than the previous term.
Next term is 10 which is 5 more than the previous term.
Next term is 17 which is 7 more than the previous term.
Next term is 26 which is 9 more than the previous term.
Hence, we can see a pattern here that the difference between two consecutive terms is a consecutive odd number. That means 3, 5, 7, 9 . . .
Therefore the next term will be 11 more than the previous term that is $ 26 + 11 = 37 $ .
Next term will be 13 more than the previous number that is $ 37 + 13 = 50 $ .
Next term will be 15 more than the previous number that is $ 50 + 15 = 65 $ .
Hence the sequence is $ 2,5,10,17,26,37,50,65 $ .

Note: As we discussed earlier, there can be multiple patterns to this question. Another pattern behind this sequence is that each term can be given by the formula $ {n^2} + 1 $ .
For example: the first term will be $ {n^2} + 1 = 1 + 1 = 2 $ .
So, 6th 7th and 8th term of the sequence will be $ {6^2} + 1 = 36 + 1 = 37 $ , $ {7^2} + 1 = 49 + 1 = 50 $ and $ {8^2} + 1 = 64 + 1 = 65 $ .