The sum of first 8 terms of geometric series is 16400 if the common ratio is 3, determine the first term?

Question

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Answer 1

assuming that 'x' is the first term, the sum of the firtst 8 terms of this geometric series may be written as :

x + 3x + 9x + 27x + ... + x.(3^(8-1)) = 16400

then :

16400 = x . (1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187) = x .(3280)
x = 16400/3280
x = 5

first term = 5

Answer 2

(a-a*r^9)/(1-3)=16400
a(1-r^9)=-32800
a*-19682=-32800
a=approximately 1.666