Question

Find the 31^st term of an A.P. whose 11^th term is 38 and the 16^th term is 73.

Answer 1

Given that,

a₁₁ = 38

a₁₆ = 73

We know that,

a_n = a + (n − 1) d

a₁₁ = a + (11 − 1) d

38 = a + 10d               ...(1)

Similarly,

a₁₆ = a + (16 − 1) d

73 = a + 15d                     ...(2)

On subtracting (1) from (2), we obtain

35 = 5d

d = 7

From equation (1),

38 = a + 10 × (7)

38 − 70 = a

a = −32

a₃₁ = a + (31 − 1) d

= −32 + 30 (7)

= −32 + 210

= 178

Hence, 31^st term is 178.