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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
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