Solution for Problem 8.3.3

Find the nth term of the following geometric sequence   1, 5, 25, 125, 625, ...
Then find the 7th term.

Solve Step

r = 625 ÷ 125 = 5r = 125 ÷ 25 = 5
r = 25 ÷ 5 = 5,        r = 5 ÷ 1 = 5,

Find the common ratio
r = 5

an = a1rn - 1 

Use the formula for geometric sequence. 

a1 = 1 and   r = 5

a1 = 1 is the first term of the sequence.

an = (1)5n - 1 = 5n - 1

nth term

a7 = (1)57 - 1 = 57 - 1 = 56 = 15,625

7th term
 Spot Check

a1 = 51 - 1 = 50 = 1

a3 = 53 - 1 = 52 = 25

a5 = 55 - 1 = 54 = 615