# maths

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the 3rd term of a g.p is 63 while the 5th term is 567,what is the sum of the first 7 terms

• maths -

t(5) = ar^4 = 567
t(3) = ar^2 = 63

divide first equation by the second

ar^4/(ar^2) = 567/63
r^2 = 9
r = ± 3

if r = ±3,
ar^2= 63
a = 7

Since you only want 7 terms, it would probably be faster to just find them and add them up

that is,
7 + 21 + 63 + 189 + 567 + 1701 + 5103 = 7651

or 7 - 21 + 63 - 189 + 567 - 1701 - 5103 = ......

or by formula
if a=7, r= 3
sum(7) = 7(3^7 - 1)/(3-1) = 7651

or if x=-3
sum(7) = 7((-3)^7 - 1)/(-3-1) = .....

• maths -

The third term of a g p is 63 while the 5th term is 567 what is the sum of the first seven terms

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