Question

Write an explicit rule for the nth term of
7, 9, 13, 21, 37
man how?

Answer 1

as per the question the nth term is 7,9,13,21,37,69.

Explanation:

By looking at the consecutive numbers We can understand, the difference of consecutive terms of given series: 7, 9, 13, 21, 37,… forms a G.P.: 2, 4, 8, 16, 32, …. And more.

So when we subtract the first term from the second term we get:

9−7=2 and after doing the same for the following numbers we get: -

13−9=4

21−13=8

37−21=16

Let the nth term be x,

x−37=32 and now solve this equation to get the nth term∴x=32+37

=69

hence the next term is 69