Answer:
First day, N(1) = 4
Second day, N(2) = 4 + 3 = 7
Third day, N(3) = 4 + 6 = 10
Fourth day, N(4) = 4 + 9 = 13
Fifth day, N(5) = 4 + 12 = 16
Explanation:
She spent 5 days on her vacation.
She collected 50 seashells in those days. Each day she collected 3 more than the previous day.
We can represent this with an arithmetic progression:
N(n) = x + 3(n - 1)
Where x is the amount of sea shells collected on the first day.
n = the particular day
So, for the five days day:
N(1) = x + 3(1 - 1) = x + 3(0) = x
N(2) = x + 3(2 - 1) = x + 3(1) = x + 3
N(3) = x + 3(3 - 1) = x + 3(2) = x + 6
N(4) = x + 3(4 - 1) = x + 3(3) = x + 9
N(5) = x + 3(5 - 1) = x + 3(4) = x + 12
The sum of all the sea shells is 50:
N(1) + N(2) + N(3) + N(4) + N(5) = 50
=> x + x + 3 + x + 6 + x + 9 + x + 12 = 50
5x + 30 = 50
5x = 50 - 30 = 20
x = 20 / 5
x = 4
Therefore:
First day, N(1) = 4
Second day, N(2) = 4 + 3 = 7
Third day, N(3) = 4 + 6 = 10
Fourth day, N(4) = 4 + 9 = 13
Fifth day, N(5) = 4 + 12 = 16