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Question

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


A
19
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B
21
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C
38
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D
42
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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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