# 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 $a,\,a+d,\,a+2d,\,a+3d,\,a+4d$

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