Question

What is the 8th term of the geometric sequence 4, −20, 100, …? −312,500 −12,500 62,500 1,562,500?

Answer 1

Let us first check the common ratio for this Geometric series .

-20/ 4= -5

100/-20 = -5

Ratio of any term with it's previous term is -5 so that is the common ratio here .

here first term a= 4 and common ratio r= -5

we know nth term of geometric series is an= a r^(n-1)

let us plug n= 8 a= 4 and r= -5 a8 = 4 ( -5)^(8-1)

a8 = 4 (-78125) = -312500

Answer : -312500

Answer 2

The first term of GP, a=4

Common ratio=
`(a2)/(a1)`=
`(-20)/(4)`=-5

r=-5

nth term of GP, an=a
`r^(n-1)`

a8=4*
`(-5)^(8-1)`

a8=4*
`(-5)^(7)`

a8=4*-78125

a8=-312500