This is question 4 from the Test of Mathematics for University Admission practice paper by the University of Cambridge.
The sequence does look a bit scary at first glance, but fret not, writing out the first few terms will help you find the summation from n = 1 to 39.
Now I did this in my head, but if you’d like, you can grab a pen and a piece of paper, and give this problem a go.
When you are ready, keep reading for the solution!
Solution
Let’s write out the first 4 terms.
The pattern is clear (and as a challenge, prove to me in the comments that the pattern holds true for later terms):
The sequence goes like -3, 3, -3, 3, -3, 3, and so on.
So the sum of each pair of terms is zero.
So we can sum up the terms as follows:
