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48. Find the sum ot tws filduie teimINCERI EXBVI49 If on1 -1)h term of an A.P is twice the (r +1lyth term, prove that (3m + 1)h term is twice the(m +n+1)h term.i u torms with first term a and nth term I show that the sum of the |
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Answer» Let a is the first term of AP and d is the common difference of APnow ,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 |
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