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Question

In an A.P., S5+S7=167 and S10=235, then find the A.P., where Sn denotes the sum of first n terms.

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Solution

s10=235s10=102(2a+(101)d]235=5(2a+9d]47=2a+9da=479d2s5+s7=16752[2a+(51)d]+72[2a+(71)d]=16752[2a+4d]+72[2a+6d]=1675[a+2d]+7[a+3d]=1675a+10d+7a+21d=16712a+31d=16712(479d2)+31d=16728254d+31d=16723d=115d=5a=479(5)2=1
AP is 1,6,11,16,.....

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