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Question

If five times the fifth term of an A.P. is equal to 8 times its eighth term, show that its 13th term is zero.


Solution

Let a1, a2, a3..... an.... be the A.P. with its first term = a and common difference = d.

It is given that

                  5a5 = 8a8

                  5(a+4d)=8(a+7d)

                   5a+20d=8a+56d

                  3a+36d=0

                  3(a+12d)=0      

                 a+12d=0

                  a+(131)d=0

                 a13=0

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