Question

The 4th term of the geometric sequence is 27 and the 7th term is 1. What is the 1st term?

Answer 1

Nth term of a G.P. is given by ar^(n - 1); where a is the first term.

4th term => 27 = ar^(4 - 1) = ar^3 . . . (1)
7th term => 1 = ar^(7 - 1) = ar^6 . . . (2)

7th term/4th term => 1/27 = ar^6/ar^3 = r^(6 - 3) = r^3
r^3 = 1/27
r = 1/3

From (1), a(1/3)^3 = 27
1/27 a = 27
a = 27 x 27 = 729

Therefore, the first term is 729.