If `a_1, a_2, a_3`,........ are in A.P. such that `a_1 + a_5 + a_10 + a_15 + a_20 + a_24 = 225`, then `a_1 + a_2+ a_3 + ......+ a_23 +a_24` is equal to

Options

A. 909
B. 75
C. 750
D. 900

Answer

D

Explanation

We have,
`a_(1)+a_(5)+a_(15)+a_(20)+a_(24)=225`
`rArr" "(a_(1)+a_(24))+(a_(5)+a_(20))+(a_(10)+a_(24))=225`
`rArr" "3(a_(1)+a_(24))=225rArra_(1)+a_(24)=75`
`:." "a_(1)+a_(2)+a_(3)+ . . .+a_(24)=(24)/(2)(a_(1)+a_(24))=12xx75=900`