sorry for before it is my first time using this website and this is the real question

Question

in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62813. How many terms are in the series?

Answer 1

t1 = 23 ---> a = 23
t3 = 92 --->ar^2 = 92
divide them
r^2 = 4
r = ± 2

sum(n) = a(r^n - 1)/(r-1) = 62813

If r = 2
23( 2^n - 1)/(2-1) = 62813
2^n - 1 = 2731
2^n = 2732

but ....
n has to be a whole number, since it stands for the number of terms
2732 is NOT a power of 2,
so even though you typed it again with a correction , the question is still flawed.

Answer 2

Answer is 13 terms