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Question
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
Options
5
6
7
8
Solution
6
\[a = 1, a_n = 11, S_n = 36\]
\[\]
\[ \because a_n = 11\]
\[ \Rightarrow a + \left( n - 1 \right)d = 11\]
\[ \Rightarrow 1 + \left( n - 1 \right)d = 11\]
\[ \Rightarrow \left( n - 1 \right)d = 10 . . . . . \left( 1 \right)\]
\[\text { Also, } S_n = 36\]
\[ \Rightarrow \frac{n}{2}\left\{ 2a + \left( n - 1 \right)d \right\} = 36\]
\[ \Rightarrow n\left\{ 2 + 10 \right\} = 72 \left( \text { Using } (1) \right)\]
\[ \Rightarrow n = 6\]
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