The sum of the first n terms of a linear sequence is \(S_{n} = n^{2}...
FURTHER MATHEMATICS
WAEC 2008
The sum of the first n terms of a linear sequence is \(S_{n} = n^{2} + 2n\). Find the common difference of the sequence.
- A. 5
- B. 4
- C. 3
- D. 2
Correct Answer: D. 2
Explanation
\(S_{n} = \frac{n}{2}(2a + (n - 1)d \)
\(\frac{n}{2}(2a + (n - 1) d = n^{2} + 2n\)
\(n(2a + (n - 1) d = 2n^{2} + 4n\)
\(2an + n^{2}d - nd = 2n^{2} + 4n\)
Comparing the equations, d = 2 (coefficient of \(n^{2}\)).
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