KEAM 2013 Math Paper

Given,
Sn= Sum of first n terms of an AP
Let a and d be the first term and common difference of an AP.
∴‌‌S4=‌

4

2

[2a+(4−1)d]=−34
(∵Sn=‌

n

2

[2a+(n−1)d])
⇒‌‌2a+3d=−17.....(i)
and ‌‌S5=‌

5

2

[2a+(5−1)d]=−60
⇒‌‌2a+4d=−24....(ii)
On subtracting Eq. (i) from Eq. (ii), we get
d=−7
Then, from Eq. (i), 2a−21=−17
⇒‌‌2a=4⇒a=2
Hence, common difference, d=−7 and first term =2