Question

Find an explicit rule for the nth term of the sequence.

The second and fifth terms of a geometric sequence are 20 and 1280, respectively.

Answer 1

Step-by-step explanation:

in a geometric sequence there is a constant factor x that is multiplied with every previous term to create the next one.

a2 = 20

a5 = 1280 = a2×x×x×x = a2×x³ = 20x³

64 = x³

x = 4

=> a1 = 5

therefore

an = an-1×4 =

$a1 \times {4}^{n - 1}$

n > 1