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

Question

Philoid · Accepted Answer

Given: a_{(m +1)} =2a_{(n +1)}

To Prove: a_{(3m + 1)} =2a_{(m +n +1)}

Proof: a_{(m +1)} =2a_{(n +1)}

a + (m + 1 – 1) d = 2a + 2(n +1 -1)d

-a=2nd – md

a=md- 2nd …(i)

LHS: a_3m+1= a + (3m +1 -1)d =md – 2nd +3md=2d(2m -n)

RHS: 2[a +(m +n +1 -1)d]= 2[md -2nd +md +nd]=2d(2m-n)

Since, LHS=RHS

Hence, proved