The 8th term of a GP is -7/32.find it's common ratio if it's first term is 28
Answers
Step-by-step explanation:
Given :-
The 8th term of a GP is -7/32
It's first term is 28
To find :-
Find it's common ratio ?
Solution :-
Given that
First term (a) = 28
The 8th term of a GP = -7/32
We know that
If a is the first term and the common ratio is r then nth term of a GP (an) = a×r^(n-1)
=> 8th term = a8
=> a8 = a×r^(8-1)
=> a8 = a×r^7
=> a×r^7 = -7/32
=> 28 × r^7 = -7/32
=> r^7 = (-7/32)/28
=> r^7 = -7/(32×28)
=> r^7= -1/(32×4)
=> r^7 = -1/(128
=> r^7 = -1/(2^7)
=> r^7= (-1/2)^7
On comparing both sides then
=> r = -1/2
Therefore, r = -1/2
Answer:-
The common ratio of the given GP = -1/2
Check:-
a8 = a×r^7
=> 28×(-1/2)^7
=> 28×-1/128
=> -28/128
=>-7/32
Therefore , a8 = -7/32
Verified the given relations in the given problem.
Used formulae:-
→ If a is the first term and the common ratio is r then nth term of a GP (an) = a×r^(n-1)
- n is the number of terms