Question

An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 108. Find the 45^th term of this A.P.

Answer 1

Number of term = n = 57

t₇ = 13

`=>` a + 6d = 13  ...(i)

Last term = t₅₇ = 108

`=>` a + 56d = 108  ...(ii)

Subtracting (i) from (ii), we get

50d = 95

`=> d = 95/50`

`=> d = 19/10`

Substituting value of d in (i), we get

`a + 6 xx 19/10 = 13`

`=> a + 57/5 = 13`

`=> a = 13 - 57/5`

= `(65 - 57)/5`

= `8/5`

`=>` General term = t_n

= `8/5 + (n - 1) xx 19/10`

`=> t_45 = 8/5 + 44 xx 19/10`

= `8/5 + 418/5`

= `426/5`

= 85.2