Question

If the 3rd and 7th terms of an A.p. are 18 and 30 respectively, find the series

Answer 1

Let,

the first term of A.P be 'a'

and common difference be 'd'.

Given,

3rd term of A.P is 18

$t_n=a+(n-1)d\\\\t_3=a+(3-1)d\\\\18=a+2d\\\\a=18-2d\:\:\:\:\:(i)$

Given, 7th term of A.P is 30

$t_7=a+(7-1)d\\\\30=a+6d\\\\30=(18-2d)+6d\:\:\:from (i)\\\\30-18=6d-2d\\\\12=4d\\\\\underline {d=3}\\\\\\a=18-2d\\\\a=18-6=12\\\\\underline{a=12}$

The series is

a, a+d,(a+2d), (a+3d), (a+4d)...

12,15,18,21,24,27,30,33,36...