Math, asked by raunakraj271296, 6 months ago

Sum of first m terms of an AP is 0. If the first term
is given by a, then the sum of next n terms is
an(m,n)
(1)
2an(m,n)
m+1
(2)
1-m
an(m + n)
(3)
an(m+n)
1-m
(4)
1+m​

Answers

Answered by Divya222011091
0

Answer:

Step-by-step explanation:

ANSWER

Let a be the first term and d be the common difference of the given AP. Then,

S  

n

​  

=  

2

n

​  

[2a+(n−1)d]

Given,

S  

m

​  

=n

2

m

​  

[2a+(m−1)d]=n

2am+m(m−1)d=2n          ...........(1)

S  

n

​  

=m

2

n

​  

[2a+(n−1)d]=m

2an+n(n−1)d=2m          ..........(2)

On subtracting 2 from 1, we get,

2a(m−n)+[(m  

2

−n  

2

)−(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 (m+n) terms of the given AP

S  

m+n

​  

=  

2

m+n

​  

[2a+(m+n−1)d]

          =  

2

m+n

​  

(−2)=−(m+n)  

Hence proved.

Answered by pawankumar9608942179
0

Answer:

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