In an AP if \(a=1\), \(a_n=20\) and \(S_n=399\), then \(n\) is
19
21
38
42
We are given:
Step 1: Recall the formula for the sum of \(n\) terms of an AP:
\[ S_n = \dfrac{n}{2} (a + a_n) \]
Step 2: Substitute the given values:
\[ 399 = \dfrac{n}{2} (1 + 20) \]
Step 3: Simplify inside the bracket:
\[ 399 = \dfrac{n}{2} (21) \]
Step 4: Multiply:
\[ 399 = \dfrac{21n}{2} \]
Step 5: Remove the fraction by multiplying both sides by 2:
\[ 798 = 21n \]
Step 6: Divide both sides by 21:
\[ n = \dfrac{798}{21} = 38 \]
Therefore, \(n = 38\).