Question

The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of the A.P.

Answer 1

First term = 6

15th term = 48

Step-by-step explanation:

(i) Given: sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1:2.  

Find: first and 15th term of the A.P.

Solution:  Now S9 = 162

   162 = 9/2 (2a + 8d)

  162 * 2/ 9 = 2a + 8d

   36 = 2a + 8d

   a +4d = 18-------(1)

  a6: a13 :: 1:2

  So 2a6 = (a13)

  2(a +5d) = (a + 12d)

  2a + 10d = a + 12d

  a -2d = 0 -------(2)

Adding (1) and 2(2), we get:  3a = 18

  a = 6

  Substituting a in (2), we get 6 -2d = 0

  d = 3

  a15 = a + 14d = 6 + 14(3) = 48