Question

Determine the formula for the nth term of the sequence:

a) -2, 1, 7, 25, 79, ....

b) 0, 1, 3, 7, 15, ....

Answer 1

a) Let $a_n=3^n-2, n\ge0, n\in \Z.$ Then

$$a_0=-1, a_1=1, a_2=7, a_3=25,a_4=79,...$$

$a_n=3^n-2, n\ge0, n\in \Z$

b) Let $a_n=2^n-1, n\ge0, n\in \Z.$ Then

$$a_0=0, a_1=1, a_2=3, a_3=7,a_4=15,...$$

$a_n=2^n-1, n\ge0, n\in \Z$