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