Class 11 Maths Sequences Series | General term of GP |

**General term of GP**

Nth term of a GP is given by a_{n} = a r ^{n−1}

Thus, a, G.P. can be written as a, ar, ar^{2}, ar^{3}, … ar^{n }^{– 1}.

The series a + ar + ar^{2} + ... + ar^{n}^{–1} is called finite geometric series

The series a + ar + ar^{2} + ... + ar^{n}^{–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 a_{n} = a r ^{n−1}

3^{rd} term, a_{3} = ar^{2} = 24 ---(i)

6^{th} term, a_{6} = ar^{5} = 192 ----(ii)

Dividing (ii by (i), we get r^{3} = 8 or r=2.

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

Hence a_{10} = 6 (2)^{9} = 3072

.