BA LLB Banaras Hindu University 2019 Solved Paper

Question : 129 of 170

Marks: +1, -0

What is the sum of the first 13 terms of an arithmetic progression, if the 5 th term is 1 and the 8 th term is

-17

Solution:

Let the first term of AP be 'a' and common difference be '

d

∵ a_{n}=a+(n-1) d

∴ \;\; 1=a+4 d

.....(i)
and

-17=a+7 d

......(ii)
On subtracting Eq. (i) from Eq. (ii), we get

3 d=-18

⇒ \;\; d=-6

, then

a=25

Now,

\;\; S_{n}=\;{n}/{2}[2 a+(n-1) d]

∴ \;\; S_{13}=\;{13}/{2}[50+12(-6)][ ∴ n=13]

=\;{13}/{2}(-22)=-143

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