In one sentence, describe what the following article is about: Not every sequence begins with the numbers 0 or 1. Look at the list of numbers that you have and find the first term. This is your starting point, which can be designated using variables as a(1).  It is common in working with arithmetic sequences to use the variable a(1) to designate the first term of a sequence. You may, of course, choose any variable you like, and the results should be the same. For example, given the sequence 3,8,13,18{\displaystyle 3,8,13,18}…, the first term is 3{\displaystyle 3}, which can be designated algebraically as a(1). Find the common difference for the sequence as before. In this working example, the common difference is 8−3{\displaystyle 8-3}, which is 5. Checking with other terms in the sequence provides the same result. We will note this common difference with the algebraic variable d. An explicit formula is an algebraic equation that you can use to find any term of an arithmetic sequence, without having to write out the full list. The explicit formula for an algebraic sequence is a(n)=a(1)+(n−1)d{\displaystyle a(n)=a(1)+(n-1)d}. The term a(n) can be read as “the nth term of a,” where n represents which number in the list you want to find and a(n) is the actual value of that number. For example, if you are asked to find the 100th item in an arithmetic sequence, then n will be 100. Note that n is 100, in this example, but a(n) will be the value of the 100th term, not the number 100 itself. Using the explicit formula for your sequence, fill in the information that you know to find the term that you need. For example, in the working example 3,8,13,18{\displaystyle 3,8,13,18}…, we know that a(1) is the first term 3, and the common difference d is 5. Suppose you are asked to find the 100th term in that sequence. Then n=100, and (n-1)=99. The complete explicit formula, with the data filled in, is then a(100)=3+(99)(5){\displaystyle a(100)=3+(99)(5)}. This simplifies to 498, which is the 100th term of that sequence.
Summary: Identify the first term of the sequence. Define your common difference as d. Use the explicit formula. Fill in your information to solve the problem.

In one sentence, describe what the following article is about: In general, children are more likely to get ear infections than adults. This is because the eustachian tubes (tubes running from the middle of each ear to the back of your throat) are smaller in children and more prone to fill with fluid. Children also have weaker immune systems than adults and are also more prone to viral infections such as colds. Anything that blocks the eustachian tube can cause an ear infection. There are other risk factors for an ear infection, including:  Allergies Respiratory infections such as colds and sinus infections Infection or trouble with the adenoids (lymph tissue in your upper throat area) Tobacco smoke Excess mucus or saliva, such as that produced during teething Living in a cold climate Changes in altitude or climate Not being breastfed as an infant Recent illness Attending daycare, especially a larger daycare with many children A middle ear infection (acute otitis media) is the most common type of ear infection and hence recognizing its symptoms is very important. Middle ear infection is caused by a virus or bacteria. The middle ear is the space just behind the eardrum that contains the small bones that pass vibrations to the inner ear. When the area becomes filled with fluid, bacteria and viruses can get in and cause an infection. An ear infection often occurs after a respiratory infection such as a cold, although severe allergies may also bring one on. Symptoms of a middle ear infection include:  Ear pain or an earache Feeling of fullness in the ear Feeling ill Vomiting Diarrhea Hearing loss in the infected ear Tinnitus Dizziness Ear drainage Fever, especially in children ” Swimmers’ ear, also known as otitis externa or an “external ear infection,” is an infection of the outer ear canal caused by bacteria or fungi. Moisture is a common culprit for this type of infection (hence the name), but scratching or inserting things into the ear canal can also leave you prone to infection. Symptoms may begin as mild but often worsen, and include:  Itching in your ear canal Redness inside the ear Discomfort that worsens if you pull or push on your outer ear Ear drainage (begins clear and odorless, may progress to pus) More severe symptoms include:  Feeling of fullness or blockage Decreased hearing Severe pain that radiates outward to your face or neck Swelling of neck lymph nodes Fever Young children may display different symptoms of ear infection than older children and adults. Because young children often cannot communicate how they’re feeling, look for the following symptoms:  Tugging, pulling or scratching the ear Banging the head around Fussiness, irritability, or incessant crying Difficulty sleeping Fever (especially for infants and very young children) Fluid drainage from the ear Clumsiness or balance problems Trouble hearing Most ear infections can be treated at home, and many go away on their own. However, if you or your child experience certain symptoms, you should contact your doctor immediately. These symptoms include:  Blood or pus in ear drainage (may look white, yellow, green, or pinkish/red) Continued high fever, especially if it is over 102F (39C) Dizziness or vertigo Stiff neck Tinnitus Pain or swelling behind or around the ear Ear pain that lasts more than 48 hours
Summary:
Know who is most at risk for an ear infection. Recognize the symptoms of a middle ear infection. Distinguish between a middle ear infection and “swimmers’ ear. Look for signs of ear infection in children. Know when to seek immediate medical attention.