Question

What is the sum of a 14–term arithmetic sequence where the last term is 30 and the common difference is –5?


875

422.5

812.5

455

Answer 1

a[n] = a[1] + (n-1)d = a[1] - 5(n-1)

a[14] = a[1] - 5(14-1) = a[1] - 65
30 = a[1] - 65
a[1] = 95

sum of first 14 terms = 14(a[1] + a[14])/2 = 14(95 + 30)/2 = 875