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Question

Given $$d=5, S_9=75$$, find a 


A
353
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B
283
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C
543
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D
343
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Solution

The correct option is C $$\dfrac{-35}{3}$$
We know that sum of first $$n$$ terms,  $$S_n = \dfrac{n}{2} (2a+(n-1)d)$$, where $$a$$ & $$d$$ are the first term & common difference of an AP.
$$\therefore S_9=\dfrac {9}{2}(2a+d(9-1))$$
$$\Rightarrow 75=4.5(2a+8d)$$
$$\Rightarrow 2a+8d=\dfrac {75}{4.5}$$
$$\Rightarrow 2a=\dfrac {150}{9}-40=\dfrac {150-360}{9}=\dfrac {-210}{9}=\dfrac {-70}{3}$$
$$\Rightarrow a=\dfrac {-35}{3}$$

Mathematics

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