Question

if SN denote the sum of first n terms of aan ap what will be the value of 52-51
​

Answer 1

Answer:

Let the First term of A.P=a

And common difference =d

S  

30

​  

=  

2

30

​  

[2a+(30−1)d]

S  

20

​  

=  

2

20

​  

[2a(20−1)d]

S  

10

​  

=  

2

10

​  

[2a+(10−1)d]

R.H.S=3[S  

20

​  

−S  

10

​  

]

=3[[  

2

20

​  

(2a+20−1)d]−[  

2

10

​  

(2a+(10−1)d]]

=3[20a+190d−10a−45d]

=15(2a+29d)

=  

2

30

​  

[2a+(30−1)d]

=S  

30

​  

 

=L.H.S

Explanation:

Answer 2

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Let the First term of A.P=a

And common difference =d

S  

30

 

=  

2

30

 

[2a+(30−1)d]

S  

20

 

=  

2

20

 

[2a(20−1)d]

S  

10

 

=  

2

10

 

[2a+(10−1)d]

R.H.S=3[S  

20

 

−S  

10

 

]

=3[[  

2

20

 

(2a+20−1)d]−[  

2

10

 

(2a+(10−1)d]]

=3[20a+190d−10a−45d]

=15(2a+29d)

=  

2

30

 

[2a+(30−1)d]

=S  

30

 

 

=L.H.S

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