Q : 3      In an AP:

              (x) given  \small l=28,S=144 \ and \ n = 9  and there are total \small 9 terms. Find \small a.

Answers (1)

It is given that
\small l=28,S=144 \ and \ n = 9
Now, we know that
l = a_n = a+(n-1)d
28 = a_n = a+(n-1)d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(i)
Now, we know that 
S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow 144 = \frac{9}{2}\left \{ a + a +(n-1)d\right \}
\Rightarrow 288 =9\left \{ a+ 28\right \} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -(using \ (i))
\Rightarrow a+28= 32
\Rightarrow a=4
Therefore, value of a is 4

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