Question

If the sum of the first n terms of an AP is given by Sn=4 n2 - 3n , find the nth term of the AP.

Answer 1

Answer :

Given that the sum of the first n terms of the AP,
Sn = 4n² - 3n

Now, S(n - 1)

= 4(n - 1)² - 3(n - 1)

= 4(n² - 2n + 1) - 3(n - 1)

= 4n² - 8n + 4 - 3n + 3

= 4n² - 11n + 7

∴ nth term

= Sn - S(n - 1)

= (4n² - 3n) - (4n² - 11n + 7)

= 4n² - 3n - 4n² + 11n - 7

= (8n - 7)

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Answer 2

nth term = Sn-Sn-1.
Answer is 8n-7