Q : 3    In an AP:

            (v) given \small d=5, S_9=75, find \small a and \small a_9.

Answers (1)

It is given that
\small d=5, S_9=75
Now, we know that 
S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S_{9} = \frac{9}{2}\left \{ 2\times(a) +(9-1)5\right \}
\Rightarrow 75= \frac{9}{2}\left \{ 2a +40\right \}
\Rightarrow 150= 18a+360
\Rightarrow a = -\frac{210}{18}=-\frac{35}{3}
Now,
a_{9} = a+ 8d = -\frac{35}{3} + 8(5)= -\frac{35}{3}+40 = \frac{-35+120}{3}= \frac{85}{3}
 

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