1.

If (m+1)th term of an A.P is twice the (n+1)th term, Prove that (3m+1)th term is twice the (m+n+1)th term.

Answer»

Given

a+ md =2(a+ nd)

then a = (m-2n)d

t3m+1 = a +3md

= (m -2n)d +3md = 4nd -2nd

= 2(2m-n)n .......(1)

tm+n+1 = a +(m +n)d

= (m -2n)d + (m +n) d

= (2m -n)d .........(2)

From (1) and (2) t3m+1 = 2tm+n+1



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