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1+4+7+_____n terms = n(3n-1) ÷2 |
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Answer» \(S_n = 1 + 4 + 1 +...+ 3n - 2\) \(\begin{pmatrix}\because \text{nth term of sequence is}\\a_n = a+ (n - 1)d\\= 1+(n-1)3\\= 3n- 2\end{pmatrix}\) \(= \sum (3n - 2)\) \(= 3\sum n - 2\sum 1\) \(= \frac{3(n(n+1))}{2}-2n\) \(= \frac{3n^2+ 3n - 4n}{2}\) \(= \frac{3n^2 - n}{2}\) \(= \frac{n(3n -1)}{2}\) |
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