# If 12th term of an apbis -13 and the sum of first four term is 24 what is sum of first 10 term?

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i.e a₁₂=a₁+11d (a₁ is first term and 'd' is common difference)

Let, the first four terms of A.P is a,a+d,a+2d,a+3d

Given, sum of first four terms is 24

Then, a+(a+d)+(a+2d)+(a+3d)=24

4a+6d=24

or 2a+3d=12 (equation 1)

a₁₂=a₁+11d

-13=a₁+11d (equation 2)

On solving equation 1 and 2 , we will have

d= - 2

therefore, putting d= - 2 in equation 2 we will have a₁=9(first term)

a₁₀=a₁+9d

=9+9(-2)

= -9 (last term as per question)

Sum of ten terms is:

Formula is S₁₀= n/2 (first term + last term)

= 10/2 (9+(-9)

= 0 (zero)