Question 3 (vii)
In an AP:
(vii) Given a = 8, $a_{n} = 62$ , $S_{n} = 210$ , find n and d.

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Solution

(vii) $G i v e n t h a t, a = 8, a_{n} = 62, S_{n} = 210 A s S_{n} = \frac{n}{2} (a + a_{n}) 210 = \frac{n}{2} (8 + 62) \Rightarrow 35 n = 210 \Rightarrow n = \frac{210}{35} = 6 N o w, 62 = 8 + 5 d \Rightarrow 5 d = 62 - 8 = 54 \Rightarrow d = \frac{54}{5} = 10.8$

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