Question
In an AP: $a = 5, d = 3, a_n= 50,$ find $n$ and $S_n$.
✓
Answer
Here, $a = 5, d = 3, a_n= 50$
We know that
$ a_n=a+(n-1) d $
$ \Rightarrow 50=5+(n-1) 3 $
$ \Rightarrow(n-1) 3=50-5 $
$ \Rightarrow(n-1) 3=45 $
$ \Rightarrow n-1=\frac{45}{3} $
$ \Rightarrow n-1=15 $
$ \Rightarrow n=15+1 $
$ \Rightarrow n=16$
$\text { Again, we know that }$
$ S_n=\frac{n}{2}[2 a+(n-1) d] $
$ \Rightarrow S_n=\frac{16}{2}[2(5)+(16-1) 3] $
$ \Rightarrow S_n=8[10+45] $
$ \Rightarrow S_n=8(55) $
$ \Rightarrow S_n=440$
We know that
$ a_n=a+(n-1) d $
$ \Rightarrow 50=5+(n-1) 3 $
$ \Rightarrow(n-1) 3=50-5 $
$ \Rightarrow(n-1) 3=45 $
$ \Rightarrow n-1=\frac{45}{3} $
$ \Rightarrow n-1=15 $
$ \Rightarrow n=15+1 $
$ \Rightarrow n=16$
$\text { Again, we know that }$
$ S_n=\frac{n}{2}[2 a+(n-1) d] $
$ \Rightarrow S_n=\frac{16}{2}[2(5)+(16-1) 3] $
$ \Rightarrow S_n=8[10+45] $
$ \Rightarrow S_n=8(55) $
$ \Rightarrow S_n=440$
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