Question
In an A.P. (with usual notations) : given a = 3, n = 8, S = 192, find d.
✓
Answer
$\begin{aligned} & a =3, n =8, S =192 \\ & S _{ n }=\frac{n}{2}[2 a+(n-1) d] \\ & 192=\frac{8}{2}[2 \times 3+7 \times d] \\ & 192=4[6+7 d ] \\ & \Rightarrow \frac{192}{4}=6+7 d \\ & \Rightarrow 48=6+7 d \\ & \Rightarrow 7 d =48-6=42 \\ & d =\frac{42}{7}=6 \\ & \therefore d =6 .\end{aligned}$
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