The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

Explanation

Let the first term and common difference of the A.P. be 'a' and 'd' respectively.
`:. a_(4)+a_(8)=24`
`rArr a+3d+a+7d=24 rArr 2a+10d=24`
`rArr a+5d=12" " ...(1)`
and `a_(6)+a_(10)=44`
`rArr a+5d+a+9d=44 rArr 2a+14d=44`
`rArr a+7d=22 " " ..(2)`
Subtract equation (1) from equation (2), we get
`{:(" "a+7d""=22),(underset(-)" "a underset(-)+5d=""underset(-)12),(bar(" "2d=10" ")):}`
`rArr" " d=5`
put d=5 in eq. (1)
`a+5(5)=12 rArr a=-13`
`:. a+d=-13+5=-8`
`a+2d=-13+2xx5=-3`
Hence, first three terms of A.P. are, -12,-8,-3.