The first and 5th terms of an exponential sequence are 16 and 9 respectively. Find the 7th terms of the sum of the first 7 terms

Answer 1

from your data:
a = 16
ar^4 = 9

16r^4 = 9
r^4 = 9/16
r^2 = ± 3/4 , but assuming r is real, r^2 = 3/4
r = ±√3 / 2

if a = 16, r = √3/2
term(7) = ar^6 = ar^2 r^4 = 16(3/4)(9/16) = 27/4

sum(7) = a(r^7 - 1)/(r-1) = a(r^6 + r^5 + r^4 + r^3 + r^2 + r + 1)

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