Consider the sequence of numbers: 16;25;x;49

Question

1) What is the value of x? 2) What is the formula for the nth term if this number pattern? 3) Which term will be equal to 169?

Answer 1

Sequence is a(n) = (n+3)^2 , where n is a natural number, and a(n) is the element of the series.

So x is at position n=3, so x = a(3) = (3+3)^2 = 6^2 = 36

Also, a(k) = (k+3)^2 = 169 => k+3 = sqrt(169)

Neglecting negative value we get:

k+3=13

k =10,

so 10th term will have the value of 169