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  • Let be the nth term of an A.P. If <img alt="\sum_{r=1}^{100}a_{2r}=\alpha" src="https://learn.careers360.com

Let a_{n} be the nth term of an A.P. If \sum_{r=1}^{100}a_{2r}=\alpha and \sum_{r=1}^{100}a_{2r-1}=\beta,then the common difference of the A.P. is

Option: 1

\alpha -\beta
 


Option: 2

\beta -\alpha

 


Option: 3

\frac{\alpha -\beta }{2}


Option: 4

none of these


Answers (1)

best_answer

As we have learnt in

 

Common difference -

The fixed number by which the terms increase or decrease in an A.P.

- wherein

Denoted by d

 

 

a_{1}+a_{3}+a_{5}+........a_{199}=\beta

a_{2}+a_{4}+a_{6}+........a_{200}=\alpha

a_{2}-a_{1}+a_{4}-a_{3}+a_{6}-a_{5}........a_{200}-a_{199}=\alpha-\beta

d+d+d.......d=\alpha -\beta

d=\frac{\alpha -\beta }{100}

Posted by

manish painkra

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