How many terms of the series 25+19+13 +… are required to make the sum −20?

Question

How many terms of the series 25+19+13 +… are required to make the sum −20?

Answer 1

THis is aritmetic sequence with a₁ = 25 and common difference d = 19 - 25 = - 6.

a_n = a₁ + (n - 1)d = 25 - 6(n -1) = 31 - 6n;

S_n =n(a₁ + a_n)/2 = n(25 + 31 - 6n)/2 = 28n - 3n² = - 20; 3n² - 28n - 20 = 0; n = [28 ± √(784+ 240)]/6;

n = (28 + 32)/6 = 10