The first and third terms of a Gp are 5 and 80 respectively. What is the fourth term in solving

Answer 1

In GP n-th term:

an = a • r ⁿ⁻¹

where

a = a1 = initial value

r = common ratio

In this case:

a1= a = 5

a3 = a • r ²

a3 = 80

a • r ² = 80

5 • r ² = 80

Divide both sides by 5.

r ² = 16

r = ± √16

r = ± 4

Two solutions are possible:

r = - 4 and r = 4

First solution r = - 4

a4 = a • r ³ = 5 • ( - 4 ) ³ =

5 • ( - 64 ) = - 320

In this case GP is:

5 , - 20 , 80 , - 320...

Second solution r = 4

a4 = a • r ³ = 5 • 4 ³ =

5 • 64 = 320

In this case GP is:

5 , 20 , 80 , 320...