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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)}

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)}

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
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 & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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