Mathematics
The common ratio of a G.P., whose 4th term is 27 and 6th term is 243; is :
9
3
AP GP
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Answer
Let first term of G.P. be a and common ratio be r.
By formula,
⇒ an = arn - 1
Given,
4th term of G.P. is 27.
⇒ a4 = 27
⇒ ar4 - 1 = 27
⇒ ar3 = 27 ……..(1)
Given,
6th term of G.P. is 243.
⇒ a6 = 243
⇒ ar6 - 1 = 243
⇒ ar5 = 243 ……..(2)
Dividing equation (2) by (1), we get :
Hence, Option 2 is the correct option.
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Assertion (A): 5th of the given G.P. is .
Reason (R): If for a G.P., the first term is a, the common ratio is r and the number of terms = n, then sum of the first n term Sn = for all r.
A is true, R is false.
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Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.