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Question
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
Options
909
75
750
900
MCQ
Fill in the Blanks
Solution
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to 900.
Explanation:
We know that in an A.P. a1 + a24 = a5 + a20
= a10 + a15
= a12 + a13
So, 3(a12 + a13) = 225
⇒ a12 + a13 = 75
Therefore,
a1 + a2 + a3 + ………… + a23 + a24
= 12(a12 + a13)
= 12 × 75
= 900
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