An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three terms is 429. Find the AP

Explanation

Total number of terms (n)=37, which is odd
`:.` Middle term `=(37+1)/(2)`th term = 19th term
So, 3 middle most terms are 18th, 19th and 20th
`:. T_(18)+T_(19)+T_(20)=225`
`rArr a+17d+a+18d+a+19d=225`
`rArr 3a+54d=225 rArr a+18d=75 " " ...(1)`
Also, sum of last 3 term =429
`T_(35)+T_(36)+T_(37)=429`
`rArr a+34d+a+35d+a+36d=429`
`rArr 3a+105d=429 rArr a+35d=143 " " ...(2)`
Solving, (1) and (2), we get d=4 and a=3
`:.` Required A.P. is a, a+d, a+2d, a+3d,...
i.e., 3,3+4,3+2(4),3+3(4)
i.e., 3,7,11,15,...