Question

what is the fifth term of 2+5+10+17+_____
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Answer 1

Answer:

26

Step-by-step explanation:

The difference between two consecutive terms is the set of consecutive odd numbers from 3.

Answer 2

Answer:

26

Step-by-step explanation:

To find the answer, we experiment by considering some possibilities for the nth term and seeing how far away we are:

n = 1 2 3 4 5

n² = 1 4 9 16 25

n²+1 = 2 5 10 17 26

This is the required sequence, so the nth term is n² + 1. There is no easy way of working out the nth term of a sequence, other than to try different possibilities.

Tips: if the sequence is going up in threes (e.g. 3, 6, 9, 12...), there will probably be a three in the formula, etc. In many cases, square numbers will come up, so try squaring n, as above. Also, the triangular numbers formula often comes up. This is n(n + 1)/2 .