Question

The sum of the 4th or 8th terms of AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms of the AP.

Answer 1

Answer:

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Answer 2

Concept :

Arithmetic progression is defined as the sequence of numbers in algebra like the difference in the middle of every consecutive term is the same.

Given :

We have given $4^{th}$ , $8^{th}$ terms sum is $24$, and $6^{th}$ , $10^{th}$ terms sum is $44$.

Solution :

Now, finding the first three terms of the AP.

We know that,

$4^{th}$ , $8^{th}$ terms sum is $24$

So,

$4^{th}$ term is $a+3d$

$8^{th}$ term  is $a+7d$

Addition as:

$a+3d+a+7d=24\\2a+10d=24$

equation divided by $2$ :

$\frac{2a}{2} +\frac{10d}{2} =\frac{24}{2}\\\\a+5d=12 ...(1)$

Here,

$6^{th}$ , $10^{th}$ terms sum is $44$

So,

$6^{th}$ term is $a+5d$

$10^{th}$ term is $a+9d$

Addition as:

$a+5d+a+9d=44\\2a+14d=44$

equation divided by $2$:

$\frac{2a}{2}+\frac{14d}{2}=\frac{44}{2}\\a+7d=22 ...(2)$

by equation $(1)$ and $(2)$:

$\\a+7d=22\\\\a+5d=12\\2d=10\\d=\frac{10}{2}\\d=5$

So, the first three terms is $-13 , -8 ,$ and $-3$.

Hence, the correct answer is $-13 , -8 ,$ and $-3$.

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