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.
Let a be the first term and d be the common difference
Now, a6 / a13 =
=
2a + 10d = a + 12d
a = 2d (i)
Now sum of first n terms of A.P
Sn = [2a + (n – 1) d]
S9 = [2a + 8d]
162 = 9 (a + 4d)
a + 4d = 18
2d + 4d = 18 [Using (i)]
6d = 18
d =3
Now from (i), we get
a = 2 * 3 = 6
So, first term, a1 = a = 6
15th term, a15 = a + 14d = 6 + 14(3)
= 6 + 42 = 48
Therefore, First term is 6 and 15th term is 48