Q.

If a1,a2,a3,…,a24 are  in arithmetic progression  and  a1+a5+a10+a15+a20+a24=225 then a1+a2+a3+…+a23+a24 is equal to

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a

909

b

75

c

750

d

900

answer is D.

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Detailed Solution

Given that,  a1+a5+a10+a15+a20+a24=225⇒    a1+a24+a5+a20+a10+a15=225⇒    3a1+a24=225⇒    a1+a24=75[∵in an AP the sum of the terms equidistant from the beginning and the end is same and is equal to the sum of the first and last term] ∴ a1+a2+…+a24=n2(a+l)=242a1+a24=12×75=900  [from eq.(i)]
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If a1,a2,a3,…,a24 are  in arithmetic progression  and  a1+a5+a10+a15+a20+a24=225 then a1+a2+a3+…+a23+a24 is equal to