Question

In an ap if the 12th the term is -13 and the sum of its first four terms is 24 find the sum of its first 20 terms

Answer 1

here is your answer...

Answer 2

Sum of its first 20 term is 140.

Step-by-step explanation:

Since we have given that

12 th term = -13

So, it becomes,

$a_{12}=-13\\\\a+11d=-13$------------------(1)

Sum of its first four terms = 24

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

From eq(1) and (2), we get that

$a+11d=-13\\\\a+3d=12\\\\------------------------\\\\8d=1\\\\d=\dfrac{1}{8}\\\\d=0.125$

So, it becomes,

$a+3d=12\\\\a+3\times 0.125=12\\\\a+0.375=12\\\\a=12-0.375=11.625$

So, it becomes,

$S_{20}=\dfrac{20}{2}(a+19d)\\\\S_{20}=10(11.625+19(0.125))\\\\S_{20}=10(14)\\\\S_{20}=140$

Hence, Sum of its first 20 term is 140.

# learn more:

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 20 terms

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