# Geometric Sequence

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The product of the first five terms of a geometric progression is 32. If the fourth term is 17, compute the second term.

• Geometric Sequence -

a(ar)(ar^2)(ar^3)(ar^4) = 32
a^5 r^10 = 32
take 5th root
a r^2 = 2 ---- #1

ar^3 = 17 ----#2
divide #2 by #1
r = 17/2
sub into #1
a(17/2)^2 = 2
a(289/4) = 2
a = 8/289

term(2) = ar = (8/289)(17/2) =4/17

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