In an A.P., $a = -3$ and $S_{17} = 357$. The value of $a_{17}$ is

Question

Accepted Answer

Step 1: $$S_{17}=\frac{17}{2}\left[2a+16d\right]=17(a+8d)$$
Step 2: $17(a+8d)=357\Rightarrow a+8d=21$.
Step 3: Put $a=-3$: $-3+8d=21\Rightarrow 8d=24\Rightarrow d=3$.
Step 4: $$a_{17}=a+16d=-3+16(3)=-3+48=45$$
Answer: (C) $45$

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