Question

How many terms must be added in the A.P4,9,14,19.......To obtain 837?

Answer 1

Answer:

$837 = \frac{n}{2} (8 + (n - 1)5) \\ \\ 1674 = 8n + 5 {n}^{2} - 5n \\ \\ 5 {n}^{2} + 3n - 1674 = 0 \\ \\ 5 {n }^{2} + 93n - 90n - 1674 = 0 \\ \\ n(5n + 93) - 18(5n + 93) = 0 \\ \\ (n - 18)(5n + 93) = 0 \\ \\ n = - \frac{93}{5} (rejected) \\ \\ n = 18(✓)$