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
$ \mathrm{a}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1) \mathrm{d} $
$ \Rightarrow 50=5+(\mathrm{n}-1) 3 $
$ \Rightarrow(\mathrm{n}-1) 3=50-5 $
$ \Rightarrow(\mathrm{n}-1) 3=45 $
$ \Rightarrow n-1=\frac{45}{3} $
$ \Rightarrow \mathrm{n}-1=15 $
$ \Rightarrow \mathrm{n}=15+1 $
$ \Rightarrow \mathrm{n}=16$
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
$ \mathrm{a}_{\mathrm{n}}=\mathrm{a}+(\mathrm{n}-1) \mathrm{d} $
$ \Rightarrow 50=5+(\mathrm{n}-1) 3 $
$ \Rightarrow(\mathrm{n}-1) 3=50-5 $
$ \Rightarrow(\mathrm{n}-1) 3=45 $
$ \Rightarrow n-1=\frac{45}{3} $
$ \Rightarrow \mathrm{n}-1=15 $
$ \Rightarrow \mathrm{n}=15+1 $
$ \Rightarrow \mathrm{n}=16$
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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