A nifty method for calculating the sum of an evenly spaced arithmetic sequence.
The conundrum starts with you throwing your friend a bunch of numbers, on the surface the numbers might seem totally random but as mischievous as you are, the numbers are spaced evenly and there is a simple trick to decipher the sum in only a few moments. Let’s say the sequence you constructed to baffle your friend looks like this: 1, 6, 11, 16, 21, 26…. And you ask him/her what is the sum of the first 75 terms of this sequence.
After some head scratching, your friend starts labeling the numbers in the sequence in accordance to their position. So:
[1] = 1
[2] = 6
[3] = 11
[4] = 16
[5] = 21
[6] = 26
Since you haven’t really provided any other clue, your friend tries to find a correlation between the index (the number inside []) and the number of the sequence. He observes an interesting phenomenon:
index = 1: sequence number = 1
index = 2: sequence number = 1 + 5 = 6
index = 3: sequence number = 6 + 5 = 11
index = 4: sequence number = 11 + 5 = 16
