Find the 7th term

Question

Find the 7th term of the geometric sequence whose common ratio is 2/3 and whose first term is 4

Answer 1

The nth term of a geometric series sequence: a_n=a₁*r^n-1

1. a₁ = 1st term
2. r= ratio

we want a₁

a_n=a₁*r^n-1 =>

a₁=(4)*(2/3)^7-1 =>

a₁=(4)*(2/3)⁶ =>

a₁=(4)*(2/3)^7-1 =>

a₁= 256/729 or 0.35117

Answer 2

Explicit formula for a geometric series is a_n = a₁r^{n - 1}

In this case a₁ = 4; r = 2/3 (might be easier to use 0.6667); n - 1 = 7 - 1 = 6.

When you plug in the values to get an answer you can try it the old-fashioned way as a check: 4 x 2/3 x 2/3 x 2/3 x ...

or 4 x 0.6667 x 0.6667 x ... until you reach the 7th term, including the 4.