Final answer:
Using the arithmetic sequence sum formula S(n) = n/2 * (a1 + an), and with a1 = $50, d = $5, and n = 60, the sixth-grade class would have $11,850 after 60 days.
Step-by-step explanation:
To answer the question on how much the sixth-grade class would have after 60 days of adding $5 to an initial donation of $50, we need to use the formula for the sum of an arithmetic sequence. The sequence starts with a donation of $50 and increases by $5 each day, making it an arithmetic sequence with the common difference of $5.
The formula for the sum of the first n terms of an arithmetic sequence is given by S(n) = n/2 * (a1 + an), where S(n) is the sum of the first n terms, a1 is the first term, an is the nth term, and n is the number of terms.
In this scenario:
- a1 = $50 (initial donation)
- d = $5 (daily increase)
- n = 60 (days)
To find an, the 60th term, we use the formula an = a1 + (n - 1) * d.
Therefore, an = $50 + (60 - 1) * $5 = $50 + 59 * $5 = $50 + $295 = $345.
Now we use the sum formula to find S(60):
S(60) = 60/2 * ($50 + $345) = 30 * ($395) = $11,850.
After 60 days, the charity collection would have $11,850.