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If Sn the sum of the first n terms of an AP is given by Sn=3n^2-4n, then find its nth term and common difference

Posted by Khushwinder Singh 5 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 4 months ago

et the sum of first n terms of the A.P.=S_n
Given: Sn = 3n² – 4n ...(i)
Now,
Replacing n by (n –1) in (i), we get,
Sn – 1 = 3(n – 1)² – 4(n – 1)
nth term of the A.P. a_n = S_n – S_n – 1
∴ a_n = (3n² – 4n) – [3(n – 1)² – 4(n – 1)]
⇒ a_n = 3 [ n² – (n – 1)²] – 4 [n – (n – 1)]
⇒ a_n = 3 (n² – n²+ 2n – 1) – 4 (n – n + 1)
⇒ a_n = 3(2n –1) – 4
⇒ a_n = 6n – 3 – 4
⇒ a_n= 6n – 7
Thus, the nth term of the A.P = 6n – 7.

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