Write the 50th term of the series 2 + 3 + 6 + 11 + 18 + ...

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Solution

$We have, a_{1} = 2, a_{2} = 3 = 2 + 1, a_{3} = 6 = 2 + 1 + 3, a_{4} = 11 = 2 + 1 + 3 + 5, . . . a_{50} = 2 + 1 + 3 + 5 + . . . (50 terms) = 2 + \frac{49}{2} [2 \times 1 + (49 - 1) \times 2] (As, the terms apart 2 are in A . P . with a = 1 and d = 2) = 2 + \frac{49}{2} (2 + 48 \times 2) = 2 + \frac{49}{2} \times 98 = 2 + 49^{2} = 2 + 2401 = 2403$

So, the 50th term of the given series is 2403.

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