Class 11 Maths Sequences Series General term of GP

General term of GP

Nth term of a GP is given by an = a r n−1

Thus, a, G.P. can be written as a, ar, ar2, ar3, … arn – 1.

The series a + ar + ar2 + ... + arn–1   is called finite geometric series

The series a + ar + ar2 + ... + arn–1  +................   is  called  infinite geometric series

 

Numerical: In a G.P., the 3rd term is 24 and the 6th term is 192.Find the 10th term

Solution: Nth term of a GP is given by an = a r n−1

3rd term, a3 = ar2 = 24    ---(i)

6th term, a6 = ar5 = 192  ----(ii)

Dividing (ii by (i), we get r3 = 8  or r=2.

Substituting r = 2 in (i), we get a = 6.

Hence a10 = 6 (2)9 = 3072

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