Find the number of terms of the arithmetic sequence with a1

Find the number of terms of the arithmetic sequence with a₁ = -2, d = 1/4, and s = 21.

Solution

s_n=(n/2)(2a₁+(n-1)d)

21=(n/2)(2(-2)+(n-1)(1/4))

42= n(-4 +(n-1).25)

42=n(-4 + .25n-.25)

.25n² -4n -.25n -42=0

.25n²-4.25n -42=0

.25(n² -17n -168)=0

n²-17n -168=0

(n-24)(n+7)=0

n=24,-7

And number of terms cant be -7

Therefore the answer is n=24