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KEAM 2013 Math Paper

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Question : 22 of 120

Marks: +1, -0

Let

S_n

denote the sum of first

n

terms of an A.P. If

S_4=-34,S_5=-60

S_6=-93,

then the common difference and the first term of the A.P. are respectively

$-7,2$
$7,-4$
$7,-2$
$-7,-2$
$4,-7$

Solution:

Given,

S_{n}=

Sum of first

n

terms of an

AP

Let

a

and

d

be the first term and common difference of an AP.

\therefore \;\; S_{4}=\frac{4}{2}[2a+(4-1)d]=-34

\left(\because \;\; S_{n}=\frac{n}{2}[2a+(n-1)d]\right)

\Rightarrow \;\; 2a+3d=-17

.....(i)

and

\;\; S_{5}=\frac{5}{2}[2a+(5-1)d]=-60

\Rightarrow \;\; 2a+4d=-24

....(ii)

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

d=-7

Then, from Eq. (i),

2a-21=-17

\Rightarrow \;\; 2a=4 \Rightarrow a=2

Hence, common difference,

d=-7

and first term

=2

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