Q : 6     The first and the last terms of an AP are  \small 17 and  \small 350  respectively. If the common difference is \small 9, how many terms are there and what is their sum?

Answers (1)

It is given that
\small a=17,l=350,d=9,
Now, we know that
a_n = a+(n-1)d
350 = 17+(n-1)9
(n-1)9 = 333
(n-1)=37
n = 38

Now, we know that 
S_n = \frac{n}{2}\left \{ 2a+(n-1)d \right \}
\Rightarrow S_{38}= \frac{38}{2}\left \{ 2\times(17) +(38-1)9\right \}
\Rightarrow S_{38}= 19\left \{ 34 +333\right \}
\Rightarrow S_{38}= 19\left \{367\right \}
\Rightarrow S_{38}= 6973
Therefore, there are 38 terms  and their sun is 6973

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