Find the sum of first 24 terms of on AP `t_(1),t_(2),t_(3),"....",` if it is known that `t_(1) + t_(5) + t_(10) + t_(15) + t_(20) + t_(24)=225.`

Explanation

We know that, in an AP the sums of the terms equidistant from the beginning and end is always same and is equal to the sum of first and last term.
Then, `t_(1) + t_(24) = t_(5) + t_(20) = t_(10) + t_(15)`
but given `t_(1) + t_(5) + t_(10) + t_(15) + t_(20) + t_(24)=225`
`implies (t_(1) + t_(24)) + (t_(5) + t_(20)) + (t_(10) + t_(15))=225`
`implies 3(t_(1) + t_(24))=225`
`implies t_(1) + t_(24)=75`
`therefore S_(24)=(24)/(2)(t_(1) + t_(24))=12xx75=900`