We are told donut sales is described by an arithmetic sequence of 6 terms whose sum is 150 and common difference is 6. If we split this sequence into two groups of 3 terms, the sum of the first group will differ from the sum of the second group by
(number of terms)²×(common difference) = 3²×6 = 54
Then if x represents the number of donuts sold in the first 3 hours, the total number of donuts sold is
x + (x + 54) = 150
2x = 150 - 54
x = 96/2 = 48
The number of donuts sold in the first three hours is 48.
