Question

The sum of the 1st and the last term of an A.P is 42. The sum of all term is 420, the 2nd term is 4. What is the common difference?

Answer 1

$a + l = 42 \\ = > sum \: of \: n \: terms = \frac{n}{2} (a + l) = 420 \\ = > \frac{n}{2}(42) = 420 \\ = > \frac{n}{2} = 10 \\ = > n = 20 \\ as \: l = a + (n - 1)d \\ = > a + l = 2a + (n - 1)d = 42...eq(1)$
$second \: term \: = a + d = 4\\ = > a = 4 - d...eq(2) \\ now \: substituting \: eq(2) \: and \: n \: value \: in \: eq(1)$
We get
2(4-d)+19d=42
=>8-2d+19d=42
=>17d=36
=>d=36/17