To find how many strands are needed for a size 10 cable, I initially worked out the number needed for a n cable. To do this, I considered the number needed for a size 1 cable, a size 2 cable, etc. This gave me the sequence (from a size 1 to a size 5 cable):
1, 7, 19, 37, 61
I then worked out the nth term, using the formula an^2 + bn + c. The difference between each value is 6, 12, 18 and 24, and the difference between each of those differences is 6. "a" is therefore equal to 3 (6 / 2). I then worked out "c" by working out the 0th term. The difference between the 0th and the 1st term is 0, as the difference between the differences is 6, so "c" is equal to 1. Finally, I worked out "b" by subtracting "a" and "c from the fist term. 1 - 3 - 1 = -3, so "b" is equal to -3.
The value for a size n cable is therefore 3n^2 - 3n + 1. If we test that with a size 5 cable, it gives 75 - 15 + 1, which equals 61. The number of stands for a size 10 cable is therefore 300 - 30 + 1, which is 271.