Theory question 103
Sequences and SeriesHow many terms of the series −3 − 1 + 1 + … add up to 165?
Show the model answer
Model answer
a = −3, d = 2. Sₙ = (n/2)[−6 + 2(n − 1)] = n(n − 4) = 165.
n² − 4n − 165 = 0, (n − 15)(n + 11) = 0, so n = 15.
Explanation
Set Sₙ = 165 and solve the quadratic.