The sum of the first 2 terms of a GP is 9/8 and the sum of the last 2 terms is
1152. There are 12 terms altogether. Find the common ratio.
Answers
Given : The sum of the first 2 terms of a GP is 9/8
the sum of the last 2 terms is 1152.
There are 12 terms altogether.
To Find : the common ratio.
Solution:
Series is a , ar , ar² .. .. ..
a = 1st term
r = common ratio
The sum of the first 2 terms is 9/8
a + ar = 9/8
=> a(1 + r) = 9/8
sum of the last 2 terms is 1152.
last term = 12th = ar¹¹
2nd last term = 11th term = ar¹⁰
ar¹⁰ + ar¹¹ = 1152
=> ar¹⁰(1 + r) = 1152
=> a(1 + r) r¹⁰ = 1152
a(1 + r) = 9/8
=> (9/8) r¹⁰ = 1152
=> r¹⁰ = 1024
=> r¹⁰ = (±2)¹⁰
=> r = ±2
common ratio is 2 or - 2
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