Question

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

Answer 1

Let the A.P. be a,a+d,a+2d,... .
Middle most term `=(37+1)/(2)`th term=19th term
`rArr` Three middle most terms `-a_(18),a_(19) and a_(20)`
Given that, `a_(18)+a_(19)+a_(20)=225`
`rArr (a+17d)+(a+18d)+(a+19d)=225`
`rArr 3a+54d=225`
`rArr a+18d=75 `
and `a_(35)+a_(36)+a_(37)=429" " ...(1)`
`rArr (a+34d)+(a+35d)+(a+36d)=429`
`rArr 3a+105d=429 rArr a+35d=143`
`rArr 75-18+35d=143 " "` [from (1)]
`rArr 17d=68 rArr d=4`
Put d=4 in equation (1), we get
`a+18(4)=75 rArr a=3`
`:. A.P. =3,7,11,15, ...`