IF THE SUM OF THE first 5th term of G P is 162 and the 8th term is 4374.find the series

Answer 1

The sum of the first 5 terms is 162 gives us
a(r^5 - 1)/(r-1) = 162

the 8th term is 4374 gives us
ar^7 = 4374

divide the 2nd by the 1st ...
(ar^7) ÷ (a(r^5 - 1)/(r-1)) = 4374/162 = 27
r^7(r - 1)/(r^5 - 1) = 27
r^8 - r^7 = 27r^5 - 27
r^8 - r^7 - 27r^5 + 27 = 0

using a program I have to solve any equation gives us
r = 1 or r = 3.37081 correct to 5 decimals
but in a GP, r ≠ 1, or else all the terms are the same and my sum formula is invalid.

So if r = 3.37081 , a = .88458

so your sequence is:
.88458 , 2.98175, 10.05096, 33.87987, 114.20259, .... (btw, that sum is 162
and .8845(3.37081)^7 = 4374 , so my answer is correct)

judging by the degree of difficulty that final equation turned out to be, I suspect some type of typo

Answer 2

if the 5th term is 162
and the 8th term is 4374
then r^3 = 4374/162 = 27
That seems more likely.

Answer 3

I was going to work along those lines, but I followed his wording.
Made me work a bit harder, lol