Question

Choose the correct alternative answer for  the following question .

 In an A.P. 1^st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....

Options

• 42

• 38

• 21

• 19

Answer 1

 It is given that,
First term (a) = 1 
Last term (t_n) = 20
Sum of terms (S_n) = 399
We know that,

\[t_n = a + \left( n - 1 \right)d\]

\[ S_n = \frac{n}{2}\left( 2a + \left( n - 1 \right)d \right)\]

\[ \Rightarrow S_n = \frac{n}{2}\left( a + \left( a + \left( n - 1 \right)d \right) \right)\]

\[ \Rightarrow S_n = \frac{n}{2}\left( a + t_n \right)\]

\[ \Rightarrow 399 = \frac{n}{2}\left( 1 + 20 \right)\]

\[ \Rightarrow 399 = \frac{21n}{2}\]

\[ \Rightarrow 21n = 399 \times 2\]

\[ \Rightarrow n = \frac{798}{21}\]

\[ \Rightarrow n = 38\]