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प्रश्न
Write the 50th term of the series 2 + 3 + 6 + 11 + 18 + ...
उत्तर
We have,
\[ a_1 = 2, \]
\[ a_2 = 3 = 2 + 1, \]
\[ a_3 = 6 = 2 + 1 + 3, \]
\[ a_4 = 11 = 2 + 1 + 3 + 5, \]
\[ a_{50} = 2 + 1 + 3 + 5 + . . . \left( 50 \text { terms } \right)\]
\[ = 2 + \frac{49}{2}\left[ 2 \times 1 + \left( 49 - 1 \right) \times 2 \right] \left( \text { As, the terms apart 2 are in A . P . with a = 1 and d = 2 } \right)\]
\[ = 2 + \frac{49}{2}\left( 2 + 48 \times 2 \right)\]
\[ = 2 + \frac{49}{2} \times 98\]
\[ = 2 + {49}^2 \]
\[ = 2 + 2401\]
\[ = 2403\]
So, the 50th term of the given series is 2403.
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