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Find the Sum of the Following Serie: 2 + 5 + 8 + ... + 182 - Mathematics

Find the sum of the following serie:

 2 + 5 + 8 + ... + 182

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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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.4 | Q 2.1 | Page 30
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