Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Write the 50th Term of the Series 2 + 3 + 6 + 11 + 18 + ... - Mathematics

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

#### Solution

We have,

$a_1 = 2,$

$a_2 = 3 = 2 + 1,$

$a_3 = 6 = 2 + 1 + 3,$

$a_4 = 11 = 2 + 1 + 3 + 5,$

$a_{50} = 2 + 1 + 3 + 5 + . . . \left( 50 \text { terms } \right)$

$= 2 + \frac{49}{2}\left[ 2 \times 1 + \left( 49 - 1 \right) \times 2 \right] \left( \text { As, the terms apart 2 are in A . P . with a = 1 and d = 2 } \right)$

$= 2 + \frac{49}{2}\left( 2 + 48 \times 2 \right)$

$= 2 + \frac{49}{2} \times 98$

$= 2 + {49}^2$

$= 2 + 2401$

$= 2403$

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 21 Some special series
Q 7 | Page 19