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Question

Find a1+a6+a11+a16 if it is known that a1,a2.... is an A.P. and a1+a4+a7+...+a16=147.

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Solution

We have a1,a2,... in A.P. with common difference d.
So,a1+a4+a7+...a16=147
a1+(a1+3d)+...+(a1+15d)=147
6a1+3d(1+2+...+5)=147
6a1+45d=147
2a1+15d=49
Now, a1+a6+a11+a16=4a1+30d=2(2a1+15d)=98

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