Question

# In an AP if $$a = 1$$, $${ a }_{ n }=20$$ and $${ S }_{ n }=399$$, then $$n$$ is

A
19
B
21
C
38
D
42

Solution

## The correct option is B $$38$$$$a = 1$$$$a_n = 20$$$$S_n= 399$$Then,$$\Rightarrow a_n=a+(n-1)d$$$$\Rightarrow 20=1 + (n-1)d$$$$\Rightarrow 19=(n-1)d$$Also given, $$S_n = \dfrac{n}{2} \times$$$$[2a+(n-1)d]$$Substituting values, $$399\times 2=n( 2+19)$$$$\Rightarrow 798$$ = $${n\times21}$$$$n = 38$$Mathematics

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