Question

If the first term of a geometric progression be 5, common ratio be -5 and nth term is 3125, then the value of n is equal to

Answer 1

n = 5

Explanation:

the nth term of a geometric progression is

`a_(n)` = a₁
`(r)^(n-1)`

a₁ is the first term, r the common ratio , n the term number

given a₁ = 5 , r = - 5 ,
`a_(n)` = 3125 , then to solve for n

3125 = 5
`(-5)^(n-1)` ← divide both sides by 5

625 =
`(-5)^(n-1)`

`(-5)^(4)` =
`(-5)^(n-1)`

Since the bases on both sides are the same, both - 5 , then equate the exponents, that is

n - 1 = 4 ( add 1 to both sides )

n = 5