find n with first term -3, sum is 31.5 and common difference is 2.5

Question

sum of arithmetic sequence is 31.5

Answer 1

Question: find n with first term -3, sum is 31.5 and common difference is 2.5 .

A1 = -3,   Sn = 31.5,   d = 2.5

In any arithmetic sequence, the sum of the 1st n terms is given by

Sn = n(2*A1 + (n-1)d)/2

Using the information given and the formula for the sum of 1st n terms,

31.5 = n(2*(-3) + (n-1)*2.5)/2

63 = n(-6 + 2.5(n-1))

126 = n(-12 + 5n - 5)

126 = -17n + 5n^2

5n^2 - 17n - 126 = 0

(5n + 18)(n - 7) = 0

n = -18/5, n = 7   (but n must be a positive integer)

n = 7

Therefore, Answer: n = 7