Q : 3     In an AP:

                (i) given \small a=5, \small d=3,  \small a_n=50 , find \small n and \small S_n

Answers (1)

It is given that
a = 5, d = 3 \ and \ a_n = 50
Let suppose there are n terms in the AP
Now, we know that
a_n = a+(n-1)d
\Rightarrow 50 = 5 + (n-1)3
\Rightarrow 48 = 3n
\Rightarrow n = 16
Now, we know that 
S = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S = \frac{16}{2}\left \{ 2\times(5) +(16-1)(3)\right \}
\Rightarrow S = 8\left \{ 10+45\right \}
\Rightarrow S = 8\left \{ 55\right \}
\Rightarrow S =440
Therefore, the sum of the given AP  is 440

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