Question

if (m+1) th term of an Ap is twice the (n+1)th term.Prove that (3m+1)th term is twice the (m+n+1) th term

Answer 1

Hi Please find the attachment
Hope this helps.

Answer 2

Answer: Yes

Step-by-step explanation:

let a is the first term of AP and d is the common difference of AP

now ,

according to question ,

(m+1) th term =2 (n+1) th term

a+(m+1-1) d =2 {a+(n+1-1) d }

a+md=2a+2nd

(m-2n)d=a ------------(1)

now,

LHS =(3m+1) th term

=a+(3m+1-1) d

=(m-2n) d+3md

=2 (2m-n) d

RHS =2 (m+n+1) th term

=2 {a+(m+n+1-1) d}

=2 {a+(m+n) d}

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

=2 (2m-n) d

hence LHS =RHS