Question

The 3rd and 19th terms of an A.P. are 13 and 77, respectively. Find the A.P.

Answer 1

Given:

3rd term a₃ = 13

19th term a₁₉ = 77

Formula for the nth term of an A.P.:

a_n = a + (n − 1)d

Form equations:

For the 3rd term = a + 2d = 13   ...(1)

For the 19th term = a + 18d = 77   ...(2)

(a + 18d) − (a + 2d) = 77 − 13

16d = 64

d = `64/16`

d = 4

d = 4 in equation (1)

a + 2d = 13

a + 2(4) = 13

a + 8 = 13

a = 13 − 8

a = 5

a₂ = a + (n − 1)d

= 5 + (2 − 1)4

= 5 + 4

= 9

a₄ = a + (n − 1)d

= 5 + (4 − 1)4

= 5 + 12

= 17

a₅ = a + (n − 1)d

= 5 + (5 − 1)4

= 5 + 16

= 21

The A.P. is 5, 9, 13, 17, 21, ...