![]() As before, find the next number in the sequence. This one may be easier, but this time you will not get multiple choices. Look at the series, determine the pattern, and find the value of the unknown number 2. ![]() So using a different method, we’ve found that the number of pills will be zero in the sixth week, which confirms that the patient will stop taking the medicine completely in the sixth week. 11 Mathematical Sequences quizzes and 145 Mathematical Sequences trivia questions. We then add one to each side of the equation giving □ equals six. We can then divide both sides of the equation by three, giving one multiplied by □ minus one or simply □ minus one is equal to five. To find the week in which the patient will stop taking the medicine completely, we can set the general term equal to zero, because that represents the number of pills, and then solve the resulting equation to find □, the term number.įirst, we can add three multiplied by □ minus one to each side, giving three multiplied by □ minus one is equal to 15. Solution: Let a be the first term and d be the common difference of the AP. If 7 times the 7th term of an AP is equal to 11 times its 11th term, show that the 18th term of the AP is zero. So the formula for the general term is □ sub □ equals 15 minus three multiplied by □ minus one. Here are given some questions with their solutions for practice. The first term in this sequence is 15, and the common difference is negative three. And □ represents the common difference between the terms. □ or sometimes □ one represents the first term. The general term of an arithmetic sequence is given by □ sub □ equals □ plus □ minus one □, where □ sub □ represents the □th term. Here are given some questions with their solutions for practice. And so this is an example of an arithmetic sequence. As the terms decrease by the same amount each time, this means the difference between successive terms is constant. So in the sixth week, the patient will stop taking the medicine completely.Īnother way to approach this problem would be to find a formula for the general term in the sequence. In the fourth week, the patient will take nine minus three, which is equal to six pills in the fifth week, six minus three, which is three pills and finally, in the sixth week, three minus three, which is zero. So we need to continue like this until we get to zero pills. We want to find the week in which the patient will stop taking the medicine completely. In the third week, they’ll take three less again, 12 minus three which is equal to nine, so nine pills in the third week. That means in the second week, they should take three less than 15, 15 minus three which is equal to 12. There are several different ways to find the answers to the typical sequence questionsWhat is the first term of the sequence, What is the last term, What is the sum of all the termsand each has its benefits and drawbacks. The patient should then decrease the dosage, that means the number of pills they take, by three pills every week. We’re told in the question that the doctor prescribed 15 pills for the patient to take in the first week. Given that the patient should decrease the dosage by three pills every week, find the week in which he will stop taking the medicine completely. You may also see closed form sequences and sigma notation during this second year.A doctor prescribed 15 pills for his patient to be taken in the first week. In an arithmetic series the terms change by a common factor, whereas in a geometric series, they change by a common factor. In addition to binomial expansion with negative/fractional powers, you will study arithmetic and geometric series. Note that the formulae for binomial expansions is given in the formula booklet: ![]() Secondly, as mentioned above, negative/fractional powers are studied in Year 2. Firstly, positive integer powers of the expansion are studied in Year 1 – this is the only topic we study in Sequences and Series in Year 1. Binomial Expansion is studied in both years of A-Level Maths. Examples of infinite series include binomial expansions when powers of your binomial are negative or fractional or both. Of course, you can have an infinite sequence but for an infinite series to exist, the summation must converge. The difference between a sequence and a series is that the terms in a sequence are listed whereas the terms in series are summed. Recall that during GCSE Maths you were taught the nth term for linear and quadratic sequences and you also looked at compound interest. You have seen some Sequences and Series before.
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