In an AP, the sum of the first $10$ terms is $-150$ and the sum of the next $10$ terms (i.e. terms $11$ to $20$) is $-550$. Find the AP.
Step-by-Step Solution
Key Concept: Use S10 for the first equation, and (S20 - S10) for the second, then solve simultaneously.
$S_{10}=-150\Rightarrow\dfrac{10}{2}[2a+9d]=-150\Rightarrow2a+9d=-30$ — (1). [1.0 Mark]
$S_{20}-S_{10}=-550\Rightarrow S_{20}=-700$. $\dfrac{20}{2}[2a+19d]=-700\Rightarrow2a+19d=-70$ — (2). [1.0 Mark]
Subtracting (1) from (2): $10d=-40\Rightarrow d=-4$; from (1), $2a=-30+36=6\Rightarrow a=3$. So the AP is $3,-1,-5,-9,\ldots$ [1.0 Mark]
Correct Answer: