What is the units digit of the sum of the first 30 terms of the sequence 7¹, 7², 7³, . . .?
The answer is 6. Create the first few terms of the sequence: 7, 49, 343, 2401, 16807, 117649, 823543, 5764801, and you see a pattern with the units digits of these numbers in the sequence: 7, 9, 3, 1, 7, 9, 3, 1, …
This problem really is just asking to find the units digit of the sum of the first 30 terms of the repeating sequence 7, 9, 3, 1. The sum of the first 4 terms is 20, so the sum of the first 28 terms will be 7 × 20 = 140. Add to this the next two terms (the 29th and 30th terms) to get 140 + 7 + 9 = 156. So the units digit of the sum of the sequence 7¹, 7², 7³ . . . will be 6.
