What is the next three terms to a sequence -1/3125, 1/625, -1/125, 1/25
1 answer:
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Question 1.
Step 1. Add the total cost of purchasing the luxury items:
You will spend $135.85 purchasing the luxury items.
Step 2. Add the total cost of purchasing the name brand items:
You will spend $80.07 purchasing the name brand items.
Step 3. Subtract the total cost of purchasing the name brand items from the total cost of purchasing the luxury items:
Answer to the original question:
We can conclude that you will spend $55.78 more by purchasing the luxury items.
Question 2:
Part 1. To find the how many months will take to pay the card debt, we are going to use the credit card equation:
where
is the months to pay the card
is the balance
is the monthly payment
is the interest rate in decimal form
We know from our problem that the balance of the credit card is $1,367.90 and the monthly payment is $400.00, so
and 
. To find convert the interest rate to decimal form, we are going to divide the rate by 100%
.
Now that we have all we need, lets replace the values in our credit card equation:
It will take you 3.5 months according to our calculation, but since you pay $400 each month on the due date, we can conclude that it will take you 4 months to pay off the card.
Part 2. To calculate the total amount paid including the interest, we just need to multiply the monthly payment by the number of payments.
We know from our problem that the monthly payment is $400. We also know from our previous calculations that the number of payments is 4, so lets multiply both quantities:
We can conclude that the total amount paid including interest is $1,600
Step 1. Add the total cost of purchasing the luxury items:
You will spend $135.85 purchasing the luxury items.
Step 2. Add the total cost of purchasing the name brand items:
You will spend $80.07 purchasing the name brand items.
Step 3. Subtract the total cost of purchasing the name brand items from the total cost of purchasing the luxury items:
Answer to the original question:
We can conclude that you will spend $55.78 more by purchasing the luxury items.
Question 2:
Part 1. To find the how many months will take to pay the card debt, we are going to use the credit card equation:
where
We know from our problem that the balance of the credit card is $1,367.90 and the monthly payment is $400.00, so
Now that we have all we need, lets replace the values in our credit card equation:
It will take you 3.5 months according to our calculation, but since you pay $400 each month on the due date, we can conclude that it will take you 4 months to pay off the card.
Part 2. To calculate the total amount paid including the interest, we just need to multiply the monthly payment by the number of payments.
We know from our problem that the monthly payment is $400. We also know from our previous calculations that the number of payments is 4, so lets multiply both quantities:
We can conclude that the total amount paid including interest is $1,600
Answer: On the 29th day
Step-by-step explanation:
According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.
On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.
The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are lilypads on the 30th, and
lilypads on the 29th. This can be deduced multiplying succesively by 2.