The 6th term of a GP whose 4th term is 81 and the common ratio is 3
Answers
Answer:
The second term = ar = 81/2 …(1)
The fifth term = ar^4 = 1/6 …(2)
Divide (2) by (1)
r^3 = (1/6)/(81/2) = (1*2/6*81) = (1/243) or
r = 1/6.240251469 = 0.160249952 and
a = 252.7301845.
The first term is a = 252.7301845, and the common ratio is r = 0.160249952.
Question :
Find the 6th term of a G.P series whose 4th term is 81 and the common ratio is 3.
Answer :
The 6th term of the G.P series is 2187.
Given :
4th term of G.P series = 81
Common ratio (r) = 3
To find :
The 6th term of the G.P series
Solution :
We know,
The general form of G.P series for first five terms is given by:
a, ar, ar^2, ar^3, ar^4
According to the problem.
ar^3 = 81
=> a × 3^3 = 81
=> a × 9 = 81
=> a = 81/9
=> a = 9
Hence the first term is 9
Therefore the sixth term will be ar^5
= 9 × 3^5
= 9 × 243
= 2187
Hence, the 6th term of the G.P series is 2187.
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