JEE Main & Advanced Mathematics Arithmetic Progressions Selection of Terms in an A.P.

Selection of Terms in an A.P.

Category : JEE Main & Advanced

 

When the sum is given, the following way is adopted in selecting certain number of terms :

 

 

Number of terms

Terms to be taken

3

\[ad,a,a+d\]

4

\[a\text{ }3d,ad,a+d,a+\text{ }3d\]

5

\[a\text{ }2d,ad,a,a+d,a+\text{ }2d\]

 

 

In general, we take \[ard,a(r1)d,\,\,......,\,\,ad,a,a+d,\text{ }\ldots \ldots ,a+\text{ }(r1)d,\,\,a+rd,\] in case we have to take \[(2r+1)\] terms (i.e. odd number of terms) in an A.P.

 

 

And,\[a-(2r-1)d,\,a-(2r-3)d,\,.......,\] \[\,a-d,\,a+d,\,.......,\,\,a+(2r-1)d\]  in case we have to take \[2r\] terms in an A.P.

 

 

When the sum is not given, then the following way is adopted in selection of terms.

 

 

 

Number of terms

Terms to be taken

3

\[a,\,a+d,\,a+2d\]

4

\[a,\,a+d,\,a+2d,\,a+3d\]

5

\[a,\,a+d,\,a+2d,\,a+3d,\,a+4d\]

 

 

You need to login to perform this action.
You will be redirected in 3 sec spinner

Free
Videos