INPUT ARTICLE: Article: Consider all consecutive integers. Determine the number of terms (n{\displaystyle n}) in the sequence. Since you are considering all consecutive integers to 500, n=500{\displaystyle n=500}. Determine the first (a1{\displaystyle a_{1}}) and last (an{\displaystyle a_{n}}) terms in the sequence. Since the sequence is 1 to 500, a1=1{\displaystyle a_{1}=1} and an=500{\displaystyle a_{n}=500}. Find the average of a1{\displaystyle a_{1}} and an{\displaystyle a_{n}}: 1+5002=250.5{\displaystyle {
rac {1+500}{2}}=250.5}. Multiply the average by n{\displaystyle n}: 250.5500=125,250{\displaystyle 250.5 imes 500=125,250}. The first term in the sequence is 3. The last term in the sequence is 24. The common difference is 7. Determine the number of terms (n{\displaystyle n}) in the sequence. Since you begin with 3, end with 24, and go up by 7 each time, the series is 3, 10, 17, 24. (The common difference is the difference between each term in the sequence.) This means that n=4{\displaystyle n=4} Determine the first (a1{\displaystyle a_{1}}) and last (an{\displaystyle a_{n}}) terms in the sequence. Since the sequence is 3 to 24, a1=3{\displaystyle a_{1}=3} and an=24{\displaystyle a_{n}=24}. Find the average of a1{\displaystyle a_{1}} and an{\displaystyle a_{n}}: 3+242=13.5{\displaystyle {
rac {3+24}{2}}=13.5}. Multiply the average by n{\displaystyle n}: 13.54=54{\displaystyle 13.5 imes 4=54}. Mara saves 5 dollars the first week of the year. For the rest of the year, she increases her weekly savings by 5 dollars every week. How much money does Mara save by the end of the year? Determine the number of terms (n{\displaystyle n}) in the sequence. Since Mara save for 52 weeks (1 year), n=52{\displaystyle n=52}. Determine the first (a1{\displaystyle a_{1}}) and last (an{\displaystyle a_{n}}) terms in the sequence. The first amount she saves is 5 dollars, so a1=5{\displaystyle a_{1}=5}. To find out the amount she saves the last week of the year, calculate 552=260{\displaystyle 5 imes 52=260}. So an=260{\displaystyle a_{n}=260}. Find the average of a1{\displaystyle a_{1}} and an{\displaystyle a_{n}}: 5+2602=132.5{\displaystyle {
rac {5+260}{2}}=132.5}. Multiply the average by n{\displaystyle n}: 132.552=6,890{\displaystyle 132.5 imes 52=6,890}. So she saves $6,890 by the end of the year.

SUMMARY: Find the sum of numbers between 1 and 500. Find the sum of the described arithmetic sequence. Solve the following problem.

INPUT ARTICLE: Article: The button will then change to read "Unfollow." That particular contact will no longer display in your Twitter timeline.

SUMMARY: Log in to your Twitter account at https://twitter.com/. Navigate to or click on the profile of the contact you want deleted from your Twitter timeline. Point to the blue button labeled "Following" at the top of the contact's Twitter timeline. Click on the "Unfollow" button.

INPUT ARTICLE: Article: Use the tip of a chisel or knife to chip away a small piece of the plaster in an out-of-the-way area of the wall. If the brick below is intact and still has its original color, you can proceed with confidence. If it crumbles or breaks underneath your touch or looks cracked or porous, it's probably best to leave it alone. Attempting to expose deteriorated brick will only damage it further. If you're not careful, you could end up ruining the appearance of the brick or even compromising the stability of the wall. It's necessary to expose a portion of the brick in order to see if it's worth uncovering the rest. Brick doesn't always age gracefully, even when it's sealed away beneath another finishing material. To prepare for restoration, start by removing any nearby furniture, fixtures, or personal belongings from the area you'll be working in. Then, spread out one or more sheets of plastic over the floor, covering as much territory as you can. Use painter's tape to secure the edges of the plastic to the floor at the base of the wall. Taking a chisel to a plaster wall can generate a considerable amount of dust and debris. By taking a few moments to put down a protective buffer, you stand to save yourself a lot of time and energy that you might otherwise spend deep-cleaning later on. It may also be a good idea to seal off air vents and doorways close to your work area to limit the amount of dust that makes its way into other parts of your home. It's important that you use a respirator that actually filters the air to avoid breathing in lungfuls of drifting dust. An ordinary facemask won't cut it for this project. And since this project is likely to take many hours, you'll want to pull on some thick, durable gloves to keep your hands comfortable while you go to work on the plaster. Plan on wearing a change of old clothes that you don't mind ruining. You may never get all the dust out of them once you're done.

SUMMARY:
Inspect the condition of the brick you want to expose before you begin. Cover the floor below the wall with plastic sheeting. Equip yourself with a respirator, goggles, and a pair of work gloves.