A coin collector is able to collect 5 coins each day. The collector has 5 coins on the first day, 10 on the second, 15 on the third day, and so on. Which expression represents the number of coins the collector has after d days?
a) d + 5
b) 5 d
c) d5
d) 5d
The number of coins the collector has after d days can be calculated by multiplying the number of coins collected each day (5) by the number of days (d). Therefore, the correct expression is:
d * 5
This simplifies to:
5d
The number of coins the collector has on each day follows an arithmetic sequence where the first term is 5 and the common difference is 5.
To find the number of coins the collector has after d days, we use the formula for the nth term of an arithmetic sequence:
\(a_n = a_1 + (n-1)d\)
where \(a_n\) represents the nth term, \(a_1\) is the first term, n is the number of terms, and d is the common difference.
In this case, the number of days, d, corresponds to the number of terms (n).
So, the expression that represents the number of coins the collector has after d days is:
\(a_d = 5 + (d-1)5\)
Simplifying this expression gives:
\(a_d = 5 + 5d - 5\)
Which can be further simplified to:
\(a_d = 5d\)
Therefore, the correct expression that represents the number of coins the collector has after d days is option:
d) 5d