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Sum of N Terms of an AP

If for an A.P...

Question

If for an A.P., $t_{3} = 17, t_{2} = 37$ . Then find $s_{16}$ .

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Solution

Let the common difference be $d$ then
$t_{2} = 37$ ,
$t_{3} = 17$
$\Rightarrow t_{2} + d = 17$
$\Rightarrow 37 + d = 17$
$\Rightarrow d = - 20.$
So,
$t_{2} = t_{1} + d$
$37 = t_{1} - 20$
$t_{1} = 57.$

Now, using the formula of finding sum of $n$ terms
$S_{n} = \frac{n}{2} [2 t_{1} + (n - 1) d]$

$S_{16} = \frac{16}{2} [2 (57) + (16 - 1) (- 20)]$

$S_{16} = 8 [114 - 300]$
$S_{16} = - 1488.$

Hence, this is the required answer.

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