Short Answer TypeIf Sn, the sum of first n terms of an A .P. is given by Sn = 5n2 + 3n, then find its nthterm.
Sn = 5n2 + 3n
⇒ Sn – 1 = 5(n – 1)2 + 3(n – 1)
∴ Sn – Sn – 1 = (5n2 + 3n) – [5(n – 1)2 + 3(n – 1)}
⇒ an = (5n2 + 3n) – {5 (n2 – 2n + 1) + 3n – 3}
= (5n2 + 3n) – {5n2 – 10n + 5 + 3n –3}
= 5n2 + 3n – 5n2 + 7n – 2
= 10n – 2
Hence, required nth term is 10n – 2.
Find the sum of the :
(i) First 25 terms of an A .P. whose nth term is given by an= 7 – 3n
Long Answer TypeIf in sin A .P. the sum of m terms is equal to n and the sum of n terms is equal to m, then prove that the sum of (m + n) terms is –(m + n).
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