Question

If the fifteenth term if an A.P. is half the forty-first term, show that the sixty-fifth term is four times the eighth term.​

Answer 1

Answer:

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Step-by-step explanation:

now let the fifteenth term of ap be a+14d and that of its forty-first term be a+40d

moreover its sixty-fifth term be a+64d and its eighth term be a+7d

To Prove=a+64d=4(a+7d)

so now according to given condition

a+14d=1/2×(a+40d)

ie 2(a+14d)=a+40d

so 2a+28d=a+40d

ie a=12d (1)

now then using

a+64d=4(a+7d) (2)

substitute value of a from (1) in (2)

we get

12d+64d=4(12d+7d)

ie 76d=4(19d)

ie 76d=76d

hence lhs=rhs

thus proved