|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