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Question
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
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Solution
a = 8, an = 62, Sn = 210
an = a + (n – 1)d
62 = 8 + (n – 1)d
(n – 1)d = 62 – 8 = 54 ...(i)
Sn = `n/(2)[2a + (n - 1)d]`
210 = `n/(2)[2 xx 8 + 54]` ...[From (i)]
420 = n(16 + 54)
⇒ 420 = 70n
n = `(420)/(70)` = 6
∴ (6 – 1)d = 54
⇒ 5d = 54
⇒ d = `(54)/(5)`
Hence d = `(54)/(5) and n = 6`.
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