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प्रश्न
In an AP, if Sn = n(4n + 1), find the AP.
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उत्तर
We know that, the nth term of an AP is
an = Sn – Sn – 1
an = n(4n + 1) – (n – 1){4(n – 1) + 1} ...[∵ Sn = n(4n + 1)]
⇒ an = 4n2 + n – (n – 1)(4n – 3)
= 4n2 + n – 4n2 + 3n + 4n – 3
= 8n – 3
Put n = 1,
a1 = 8(1) – 3
= 5
Put n = 2,
a2 = 8(2) – 3
= 16 – 3
= 13
Put n = 3,
a3 = 8(3) – 3
= 24 – 3
= 21
Hence, the required AP is 5, 13, 21,...
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