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Question
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
Options
8
3
9
12
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Solution
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is 9.
Explanation:
Given Sn = 3n2;
Sn – 1 = 3(n – 1)2
∴ Tn = Sn – Sn–1
= 3n2 – 3(n – 1)2
= 3n2 – 3[n2 – 2n + 1] ...[∵ (a – b)2 = a2 – 2ab + b2]
= 3n2 – 3n2 + 6n – 3
= 6n – 3
∴ T2 = 6 × 2 – 3
= 12 – 3
= 9
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