If the sum of the first n terms of an AP is given by Sn -3 n2-n- find its i nth term- ii first term- and iii common difference-

Given: nbsp;Sn nbsp;= (3n2 nbsp;n) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...(i ...

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Standard X

Mathematics

nth Term of an AP

If the sum of...

Question

If the sum of the first n terms of an AP is given by Sn = (3n² − n), find its (i) nth term, (ii) first term, and (iii) common difference.

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Solution

Given: S_n = (3n² - n) ...(i)
Replacing n by (n - 1) in (i), we get:
S_n-1 = 3(n - 1)² - (n - 1)
= 3(n² - 2n + 1) - n + 1
= 3n² - 7n + 4
(i) Now, T_n = ( S_n - S_n-1)
= (3n² - n) - (3n² - 7n + 4 ) = 6n - 4
∴ n^th term, T_n = (6n - 4) ...(ii)

(ii) Putting n = 1 in (ii), we get:
T₁= (6 ⨯ 1) - 4 = 2

(iii) Putting n = 2 in (ii), we get:
T₂= (6 ⨯ 2) - 4 = 8
∴ Common difference, d = T₂ - T₁ = 8 - 2 = 6

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If the sum of the first n terms of an AP is given by Sn = (3n2 − n), find its (i) nth term, (ii) first term, and (iii) common difference.

If the sum of the first n terms of an AP is given by Sn = (3n² − n), find its (i) nth term, (ii) first term, and (iii) common difference.