Given: a12 = -13
⇒ a + 11d = -13
⇒ a = -13 – 11d …(i)
and S4 = 24
⇒ 2[-26 -22d + 3d] = 24
⇒ -26 – 19d = 12
⇒ -19d = 12 + 26
⇒ -19d = 38
⇒ d = -2
Putting the value of d in eq. (i), we get
a = -13 – 11(-2) = -13 + 22 = 9
So, a = 9 , d = -2 and n = 10
Now, we have to find the S10
⇒ S10 = 5[2×9 + 9(-2)]
⇒ S10 = 5[18 – 18]
⇒ S10 = 0
Hence, the sum of first 10 terms is 0