Question

If the sum of first m term of an ap is n terms is m then shiw that the sum of its first(m+n)terms is-(m+n)

Answer 1

here is your answer

Answer 2

Correct Question:-

•If the sum of first m term of an ap is n terms is m then show that the sum of its first (m+n) terms is-(m+n)

Concept:-

•Here, the concept of sum of n terms of AP has been used for proving the question.

Solution:-

Let Sn be the sum of n terms, a be the first term and d be the common difference of the given Arithematic progression.

•Sn=n =>m/2[2a+(m-1)d]=2n

=>2am +m(m-1) d=2n. _____( 1 )

•Sn=m =>n/2[2a+(n-1)d]=m

=>2am +n(n-1)d=2m. _____( 2 )

On subtracting (2) from (1) ,we get;

2a(m-n)+[(m²-n²)-(m-n)]d=2(n-m)

=>(m-n)[2a+(m+n-1)d]=2(n-m)

=>2a+(m+n-1)d=-2. _______( 3 )

•Sum of first (m+n) terms of the given AP

=(m+n)/2×[2a+m+n-1)d]

=(m+n)/2×[-2]=-(m+n) [using (3) ]

Hence,Proved/showed