The sum of the $4$th and $8$th terms of an AP is $24$, and the sum of the $6$th and $10$th terms is $44$. Find the AP.
Step-by-Step Solution
Key Concept: Translate both conditions into equations in a and d, then solve simultaneously.
$a_4+a_8=24\Rightarrow(a+3d)+(a+7d)=24\Rightarrow2a+10d=24\Rightarrow a+5d=12$ — (1). [1.0 Mark]
$a_6+a_{10}=44\Rightarrow(a+5d)+(a+9d)=44\Rightarrow2a+14d=44\Rightarrow a+7d=22$ — (2). [1.0 Mark]
Subtracting (1) from (2): $2d=10\Rightarrow d=5$; then from (1), $a=12-25=-13$. So the AP is $-13,-8,-3,2,\ldots$ [1.0 Mark]
Correct Answer: