sum of arithmetic sequence word problems

#SUM OF ARITHMETIC SEQUENCE WORD PROBLEMS PLUS#

This would be a perfectly acceptable form in which to leave our answer, but we’re going to choose to factor by 100.

#SUM OF ARITHMETIC SEQUENCE WORD PROBLEMS PLUS#

And distributing the parentheses gives 100𝑛 plus 100𝑛 squared. We can then cancel a factor of two throughout, which will give 𝑛 multiplied by 100 plus 100𝑛. And then simplifying further within the parentheses, we have 𝑛 over two multiplied by 200 plus 200𝑛. This simplifies to 𝑛 over two multiplied by 400 plus 200𝑛 minus 200. Substituting 200 for both 𝑎 and 𝑑 gives 𝑠 sub 𝑛 is equal to 𝑛 over two multiplied by two times 200 plus 200 multiplied by 𝑛 minus one. The common difference 𝑑 is the amount that the terms in the sequence increase by each time that’s also 200 pounds. That’s 200 pounds, or we’ll just use 200 in our formula. The first term in the sequence is the amount the restaurant gives away on day one. We don’t know how many days they’re running the campaign for, so our formula will be in terms of the unknown 𝑛. We can now use this formula to help us find a formula for the total amount the restaurant will give away. It’s 𝑠 sub 𝑛 is equal to 𝑛 over two multiplied by two 𝑎 plus 𝑛 minus one 𝑑, where 𝑠 sub 𝑛 represents the sum of the first 𝑛 terms, 𝑎, or sometimes 𝑎 one, represents the first term, and 𝑑 represents the common difference.

We should recall that there is a formula for calculating the sum of the first 𝑛 terms of an arithmetic sequence. Now, these terms, the amounts they give away every day - 200, 400, 600, 800, and so on - form an arithmetic sequence because they have a common difference of 200. We are asked to find a formula to calculate the total amount of money they give away if they run this campaign for 𝑛 days. Every day they give away two more 100-pound prizes, so 200 pound more than they gave away the day before. On the third day, they’re giving away six 100-pound prizes, so that’s 600 pounds.

The next day, they’re giving away four 100-pound prizes, so that’s 400 pounds.

On the first day, they’re giving away two 100-pound prizes, so that’s 200 pounds. Let’s look carefully at how much money the restaurant are giving away each day. If 𝑛 represents the number of days in their campaign, find a formula to calculate how many pounds they will have given away in total by the end of the campaign. They will give away four 100-pound prizes the next day, six 100-pound prizes the next day, and so on, giving away two more 100-pound prizes each day than the previous day. A fast food restaurant offers to give away two 100-pound prizes on one day.

Sum of arithmetic sequence word problems