High School

If the first term of a geometric progression is 5, the common ratio is -5, and the nth term is 3125, what is the value of n?

Answer :

Answer:

n = 5

Step-by-step explanation:

the nth term of a geometric progression is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

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

given a₁ = 5 , r = - 5 , [tex]a_{n}[/tex] = 3125 , then to solve for n

3125 = 5 [tex](-5)^{n-1}[/tex] ← divide both sides by 5

625 = [tex](-5)^{n-1}[/tex]

[tex](-5)^{4}[/tex] = [tex](-5)^{n-1}[/tex]

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