In an arithmetic series $S_{20} = - 850$ and $t_{20} = - 90$ , find $t_{1}$ .

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Solution

The correct option is A 5
Given, $S_{20} = - 850, t_{20} = - 90$
$S_{n} = \frac{n}{2} [t_{1} + t_{n}]$
$\Rightarrow - 850 = \frac{20}{2} [t_{1} + (- 90)]$
$\Rightarrow - 850 = 10 [t_{1} + (- 90)]$
$\Rightarrow - 85 = t_{1} - 90$
$\Rightarrow t_{1} = 5$

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