Question

# Given $$d=5, S_9=75$$, find a

A
353
B
283
C
543
D
343

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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