# If the 12th term of an A.P. is - 13 and the sum of the first four terms is 24, what is the sum of the first 10 terms?

Given: a12 = -13

a + 11d = -13

a = -13 – 11d …(i)

and S4 = 24

[from(i)]

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

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