Question

If the 8th term of an A.P.is 31 and the 15th term is 16 more than its 11th term, then find the A. P?

Answer 1

GIVEN

8th term of an A.P.is 31
15th term is 16 more than its 11th term

FORMULA
an = a + (n- 1)d
Where an > n th term or last term 'l'
a = first term
d = common difference
n = number of terms

STATEMENT
8th term of an A.P.is 31
a8 = a + 7d
31 = a + 7d ......... (1)

15th term is 16 more than its 11th term
a15 = a11 + 16
Where a15 = a + 14d and a11 = a + 10d
a + 14d = a + 10d + 16
(a - a) + (14d - 10d) = 16
4d = 16
d = 16 / 4
d = 4 ....... (2)

SUBSITUTE (2) in (1)
31 = a + (7 x 4)
31 = a + 28
a = 31 - 28
a = 3

A.P FORMULA
a 1 = a
a2 = a + d
a3 = a2 + d ..... and so on

Therefore, A. P is 3, 7, 11, 14,...