Question

The 5th and 8th terms of an A.P. are 56 and 95, respectively. Find the 25th term of this A.P.

Answer 1

Given:

5th term a₅ = 56

8th term a₈ = 95

Formula for the nth term of an AP:

a_n = a + (n − 1)d

Form equations using the formula

For the 5th term:

a₅ = a + (n − 1)d

= a + (5 − 1)d = 56

= a + 4d = 56   ...(1)

For the 8th term:

a₈ = a + (8 − 1)d

= a + (8 − 1)d = 95

= a + 7d = 56   ...(2)

Subtract equation (1) from (2)

(a + 7d) − (a + 4d) = 95 − 56

3d = 39

d = `39/3`

d = 13

Substitute d = 13 in equation (1):

a + 4d = 56

a + 4(13) = 56

a + 52 = 56

a = 56 − 52

a = 4

Find the 25th term:

a₂₅ = a + (25 − 1)d

a₂₅ = 4 + (25 − 1)13

a₂₅ = 4 + 24 × 13

a₂₅ = 4 + 24 × 13

a₂₅ = 4 + 312

a₂₅ = 316