there are 4 ratios from the 1st term to the 5th term
1/8 * r^4 = 162 ... r^4 = 162 / (1/8) ... r = 6
sum = [1/8 * (1 - 6^5)] / (1 - 6)
The first term of a GP is 1/8 and the fifth term is 162. Find the first five terms of the GP, then find their sum.
2 answers
Using the standard formulas
a = 1/8
term(5) = ar^4
(1/8)r^4 = 162
r^4 = 1296
r^2 = 36 , if we want only real numbers
r = ±6
if r = 6
the terms are 1/8 , 3/4, 9/2, 27, 162, ...
sum(5) = a(r^5 - 1)/(r-1) = (1/8)(7776 - 1)/5 = 1555/8
if r = -6, the terms are 1/8, -3/4, 9/2, -27, 162
sum(5) = (1/8)( (-6)^5 - 1)/(-6-1) = 1111/8
a = 1/8
term(5) = ar^4
(1/8)r^4 = 162
r^4 = 1296
r^2 = 36 , if we want only real numbers
r = ±6
if r = 6
the terms are 1/8 , 3/4, 9/2, 27, 162, ...
sum(5) = a(r^5 - 1)/(r-1) = (1/8)(7776 - 1)/5 = 1555/8
if r = -6, the terms are 1/8, -3/4, 9/2, -27, 162
sum(5) = (1/8)( (-6)^5 - 1)/(-6-1) = 1111/8