Question

In an AP, if the 12th term is -13 and the sum of its first four terms is 24, find the sum of its first ten terms.
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Answer 1

Step-by-step explanation:

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Answer 2

The sum of its first ten terms is 0.

Step-by-step explanation:

Since we have given that

12 th term = -13

So, it becomes

$a+11d=-13------------(1)\\\\2a+22d=-26------------(3)$

the sum of its first four terms = 24

so, it becomes,

$S_4=24=\dfrac{4}{2}(2a+3d)\\12=2a+3d-----------------(2)$

So, from eq(3) and (2), we get that

$2a+22d=-26\\\\2a+3d=12\\\\-----------------------------------------\\\\19d=-38\\\\d=-2$

So, a+11(-2)=-13

a-22=-13

a=-13+22

a=9

So, the sum of its first ten terms would be

$\dfrac{10}{2}(2\times 9+9\times -2)\\\\=5(18-18)\\\\=0$

Hence, the sum of its first ten terms is 0.

# learn more:

In an AP, if 12th term is -13 and the sum of its first four terms is 24, find the sum of its first ten terms

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