Question

find the sum of the first 20 terms of the ap 13, 8, 3......253

Answer 1

$a = t1 = 13 \\ t2 = 8 \\ d = t2 - t1 \\ \: \: \: \: = 8 - 13 \\ \: \: \: \: = -5 \\ s20 = \frac{n}{2}(2a + (n - 1) \times d \: \: \: \: \\ \: \: \: \: \: \: \: \: = \frac{20}{2}(2 \times 13 + (20 - 1) \times ( - 5) \\ \: \: \: \: \: \: \: \: = \frac{20}{2}(26 + 19 \times - 5) \\ \: \: \: \: \: \: \: \: = \frac{20}{2}(26 - 95) \\ \: \: \: \: \: \: \: \: \: = 10 \times - 69 \\ \: \: \: \: \: \: \: \: \: \: = - 690 \\ the \: sum \: of \: 20 \: terms \: of \: an \: ap \: is \: - 690$