Question

Find the 31^st term of an A.P. whose 10^th term is 38 and the 16^th term is 74.

Answer 1

The general term of an A.P. is given by

t_n = a + (n – 1)d

Now, t₁₀ = 38

`=>` a + 9d = 38  ...(i)

And t₁₆ = 74

`=>` a + 15d = 74  ...(ii)

Subtracting (i) from (ii), we get

6d = 36

`=>` d = 6

Substituting d = 6 in (i), we get

a + 9 × 6 = 38

`=>` a + 54 = 38

`=>` a = –16

`=>` t_n = –16 + (n – 1)(6)

`=>` t₃₁ = –16 + 30 × 6

= –16 + 180

= 164