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Question
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Solution
2 + 5 + 8 + ... + 182
Here, the series is an A.P. where we have the following:
\[a = 2\]
\[d = \left( 5 - 2 \right) = 3\]
\[ a_n = 182\]
\[ \Rightarrow 2 + (n - 1)(3) = 182\]
\[ \Rightarrow 2 + 3n - 3 = 182\]
\[ \Rightarrow 3n - 1 = 182\]
\[ \Rightarrow 3n = 183\]
\[ \Rightarrow n = 61\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ \Rightarrow S_{61} = \frac{61}{2}\left[ 2 \times 2 + \left( 61 - 1 \right) \times 3 \right] \]
\[ = \frac{61}{2}\left[ 2 \times 2 + 60 \times 3 \right]\]
\[ = 5612\]
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