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`        If the pth  and qth  terms of an AP be a and b respectively, show that the sum of the first (p+q) terms of the AP is(p+q)/2{a+b+(a-b/p-q)} `
3 years ago

Arun Kumar
IIT Delhi
256 Points
```										Hello Student,
$\\t_p=a_1+(p-1)d=a \\t_q=a_1+(q-1)d=b \\\sum t_{p+q}={(p+q)(2a_1+(p+q-1)d) \over 2} \\=>\sum t_{p+q}={(p+q)(2a_1+(p-1)d+(q-1)d+d) \over 2} \\=>\sum t_{p+q}={(p+q)(a+b+d) \over 2} \\d={ (a-b) \over (p-q)}$
Now its obvious.Substitute the values to get the answer.
Thanks & RegardsArun KumarBtech, IIT DelhiAskiitians Faculty
```
3 years ago
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