Answer: The answer is (d) 96.
Step-by-step explanation:
Let the first term of the G.P. be 'a' and the common ratio be 'r'.
Given that the 2nd term is 'ar' and the 3rd term is 'ar^2'.
Also, given that the 5th term is 8 times the 2nd term:
ar^4 = 8(ar)
r^3 = 8
r = 2
Substituting r = 2, in the equation for the 3rd term:
ar^2 = 12
a(2)^2 = 12
a = 3
So, the first five terms of the GP are:
a, ar, ar^2, ar^3, ar^4
= 3, 6, 12, 24, 48
Now, to find the 6th term:
ar^5 = 96
3(2)^5 = 96
6th term = 96
Therefore, the answer is (d) 96.
I hope this helps!
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Answers & Comments
Answer: The answer is (d) 96.
Step-by-step explanation:
Let the first term of the G.P. be 'a' and the common ratio be 'r'.
Given that the 2nd term is 'ar' and the 3rd term is 'ar^2'.
Also, given that the 5th term is 8 times the 2nd term:
ar^4 = 8(ar)
r^3 = 8
r = 2
Substituting r = 2, in the equation for the 3rd term:
ar^2 = 12
a(2)^2 = 12
a = 3
So, the first five terms of the GP are:
a, ar, ar^2, ar^3, ar^4
= 3, 6, 12, 24, 48
Now, to find the 6th term:
ar^5 = 96
3(2)^5 = 96
6th term = 96
Therefore, the answer is (d) 96.
I hope this helps!