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  4. The sum 2 × 5+5 × 9+8 × 13+ ldots 10 terms is

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Q. The sum $2 \times 5+5 \times 9+8 \times 13+\ldots 10$ terms is

Sequences and Series

Solution:

$S =2 \times 5+5 \times 9+8 \times 13+\ldots 10 \text { terms } $
$ t_{r} =(3 r-1)(4 r+1) $
$=12 r^{2}-r-1 $
$\therefore S= \displaystyle\sum_{r=1}^{10}\left(12 r^{2}-r-1\right)$
$=12 \frac{10 \cdot 11 \cdot 21}{6}-\frac{10 \cdot 11}{2}-10$
$=10\left(462-\frac{11}{2}-1\right)$
$=4555$