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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