If sum of first n terms of an AP is given by 3n square -4n ,find nth t

1.	If sum of first n terms of an AP is given by 3n square -4n ,find nth term of an ap
Answer» S_n = 3n² - 4n ⇒ S_n-1 = 3(n - 1)² - 4(n - 1) ∴ S_n - S_n-1 = (3n²- 4n) - {3(n - 1)²- 4(n-1)} ⇒ a_n = (3n²- 4n)- {3(n²- 2n + 1) - 4n ± 4} = 3n² - 4n - {3n²- 6n + 3 - 4n + 4} = 3n² - 4n - {3n² -10n + 7} = 3n²- 4n - 3n²+ 10n - 7 = 6n - 7 Hence, required n^th term is 6n - 7.

If sum of first n terms of an AP is given by 3n square -4n ,find nth term of an ap

Answer»

S_n = 3n² - 4n

⇒ S_n-1 = 3(n - 1)² - 4(n - 1)

∴ S_n - S_n-1 = (3n²- 4n) - {3(n - 1)²- 4(n-1)}

⇒ a_n = (3n²- 4n)- {3(n²- 2n + 1) - 4n ± 4} = 3n² - 4n - {3n²- 6n + 3 - 4n + 4}

= 3n² - 4n - {3n² -10n + 7}

= 3n²- 4n - 3n²+ 10n - 7

= 6n - 7

Hence, required n^th term is 6n - 7.

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If sum of first n terms of an AP is given by 3n square -4n ,find nth term of an ap

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