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, 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 an = a r n−1 3 rd term, a3 = ar 2 = 24---( i) 6 th term, a6 = 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 a10 = 6( 2) 9 = 3072
Sum of terms of a GP:
Sn = a( 1-r n) /( 1-r) or Sn = a( r n-1) /( r-1) Numerical: Find sum of first 5 terms of geometric series 1, 2 / 3, 4 / 9 …. Solution: in this case a = 1, r = 2 / 3
Sn = a( 1-r n) /( 1-r)
S5 = a( 1-r 5) /( 1-r) Or S5 = 1( 1 –( 2 / 3) 5)/( 1-2 / 3) = 211 / 81