Dave started his coin collection with 25 coins. the first wee he added 2 coins, the next week he added 4 coins, and the third wee he added 6 coins. If Dave continues adding coins in the same way, how many coins will he have in his collection after one year (52 weeks)?
My answer is 2781, is this correct?
That's what I get, too.
To find the total number of coins Dave will have after one year, we can calculate the sum of the coins added each week.
In this case, Dave starts with 25 coins and adds 2 coins in the first week, 4 coins in the second week, and 6 coins in the third week. The number of coins added each week follows an increasing arithmetic sequence.
The formula to calculate the sum of an arithmetic sequence is:
Sum = (n/2) * (first term + last term),
where "n" is the number of terms in the sequence.
Let's break down the number of coins added each week:
Week 1: 2 coins
Week 2: 4 coins
Week 3: 6 coins
Week 4: 8 coins
Week 5: 10 coins
...
Week n: (n * 2) coins
To determine the number of terms in the sequence, we need to find the value of "n" when the number of coins added reaches 52 weeks. We can do this by solving the following equation:
52 = n * 2
Dividing both sides by 2, we get:
n = 26
Now we can calculate the sum of the coins added each week:
Sum = (26/2) * (2 + last term)
Since the last term is the number of coins added in the last week (Week 26), we can substitute that with "last term = n * 2":
Sum = (26/2) * (2 + 26 * 2)
Simplifying the equation further:
Sum = 13 * (2 + 52) = 13 * 54 = 702
Adding this sum to the initial number of coins Dave had, we get:
Total number of coins after one year = 25 + 702 = 727.
Therefore, the correct answer is 727, not 2781.