Gerald reads 120 pages of a book in 4 days. If he always reads 6 more pages than the previous day,find the number of pages he reads on the first day.

arithmetic sequence with d = 6

and sum of 4 terms = 120

(4/2)(2a + 3d) = 120
2(2a + 18) = 120
2a + 18 = 60
2a = 42
a = 21

To find the number of pages Gerald reads on the first day, we can use algebra.

Let's assume that Gerald reads x pages on the first day.

On the second day, he reads 6 more pages than the first day, so he reads x + 6 pages.
On the third day, he reads 6 more pages than the second day, so he reads (x + 6) + 6 = x + 12 pages.
On the fourth day, he reads 6 more pages than the third day, so he reads (x + 12) + 6 = x + 18 pages.

To find the total number of pages he reads in four days, we add up the pages he reads on each day:
x + (x + 6) + (x + 12) + (x + 18) = 120.

Simplifying the equation: 4x + 36 = 120.
Subtracting 36 from both sides: 4x = 84.
Dividing both sides by 4: x = 21.

Therefore, Gerald reads 21 pages on the first day.