Answer:
26 terms
Explanation:
The n-th term of this sequence with a common difference of 5 and a first term of -2 is ...
an = -2 +5(n -1)
The sum of the first n terms is ...
(a1 +an)/2·n = (-2 -2 +5(n -1))/2 ·n = 1573
n(5n -9) = 3146
5n^2 -9n -3146 = 0 . . . . . quadratic in standard form
Using the quadratic formula, we can find the positive solution for n to be ...
n = (9+√((-9)^2-4(5)(-3146)))/(2·5) = (9+√63001)/10 = 260/10 = 26
26 terms must be added to give the desired sum.
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Relevant formulas are ...
Sn = n(2a1 +d(n-1))/2 . . . . sum of n terms of arithmetic sequence with first term a1 and common difference d
x = (-b±√(b^2 -4ac))/(2a) . . . . . solutions to ax^2 +bx +c = 0