Multiple choice

If the sum of first $n$ terms of a series be $5n^{2}+2n$ , then its second term is:

  1. $16$
  2. $17$
  3. $\dfrac{27}{14}$
  4. $\dfrac{56}{15}$
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B Correct answer
Explanation

Sum of n terms Sn = 5n^2 + 2n. First term a1 = S1 = 5(1)^2 + 2(1) = 7. Sum of two terms S2 = 5(2)^2 + 2(2) = 20 + 4 = 24. Second term a2 = S2 - S1 = 24 - 7 = 17.

AI explanation

The sum of the first n terms is given by the formula S_n = 5n^2 + 2n. To find the second term, calculate the sum of the first two terms: S_2 = 5(2)^2 + 2(2) = 24. The first term is S_1 = 5(1)^2 + 2(1) = 7, so the second term is 24 - 7 = 17.

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