In an A.P., given a = 3, n = 8, S = 192, find d.

Given,

a = 3, n = 8.

By formula,

Sum of n terms = $\dfrac{n}{2}[2a + (n - 1)d]$

S = 192

Substituting values we get :

$\Rightarrow \dfrac{8}{2}[2 \times 3 + (8 - 1) \times d] = 192 \\[1em] \Rightarrow 4[6 + 7d] = 192 \\[1em] \Rightarrow 6 + 7d = \dfrac{192}{4} \\[1em] \Rightarrow 6 + 7d = 48 \\[1em] \Rightarrow 7d = 42 \\[1em] \Rightarrow d = \dfrac{42}{7} = 6.$

Hence, d = 6.