11.3 GEOMETRIC SEQUENCES AND SERIES CLASSZONE


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You can tell if a sequence is arithmetic if the difference between all pairs of consecutive terms, a n – a n – 1 , is constant. Finally, try to find a relationship between the previous value, a n – 1 , and the term number, n. Suppose you were looking at the following sequence:. You know the value of all the variables in this formula except n , so you can solve for the number of terms in the series. You must know the beginning term of a sequence as well as some other information in order to determine a recursive rule. Suppose you were looking at the following sequence: After substituting for terms you know, write the equation in standard form, factor and solve for n. Help for Exercises on page A recursive rule tells how consecutive values of a sequence are related.

Another technique is to try to see if a relationship exists between a term of the sequence and the previous two terms of the sequence. Since n represents the number of terms in the series, reject solutions that are negative integers. For example, 3, 3, 6, 9, 15, 24, 39, In order to answer part a of these exercises, you must first determine a n before applying the formula for the sum of an arithmetic series. In this case you find the value of a term in a sequence by multiplying the preceding term by the common ratio, r. In other words, the value of any term in a sequence can be found by adding the common difference, d, to the preceding term. Notice that the third term 7 can be found by taking the second term 4 and adding 3 and that the fourth term 11 can found by taking the third term 7 and adding 4. You must know the beginning term of a sequence as well as some other information in order to determine a recursive rule.

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CHEAT SHEET

Sequences and Series The sequence 2, 2, 4, 8, 32,For example, 3, 3, 6, 9, 15, 24, 39, You know geoometric value of all the variables in this formula except nso you can solve for the number of terms in the geomegric.

In order to answer part a of these exercises, you must first determine a n before applying the formula for the sum of an arithmetic series.

Since you also don’t know the number of terms in the series, you can’t directly solve for a n. Another technique is to try to see if a relationship exists between a term of the sequence and the previous two terms of the sequence. Difference between terms While checking to see if the sequence is arithmetic, you notice that the difference between consecutive terms keeps increasing by one.

Notice that the third term 7 can be found by taking the second term 4 and adding 3 and that the fourth term 11 can found by taking the third term 7 and adding 4. Help for Exercises on page In order to answer part a of these exercises, you must first determine a n before applying the formula for the sum of an arithmetic series. Test Practice Problem of the Week. If a sequence cannot be classified as arithmetic or geometric, then you must determine the recursive rule using some educated guesswork.

In part b of these exercises, you are given the sum of a series and you are being asked to find the number of terms in the series. Test Practice Problem of the Week.

Suppose you were looking at the following sequence: Since n represents the number of terms in the series, reject solutions that are negative integers. You must know the beginning term of a sequence as well as some other information in order to determine a recursive rule. Help for Exercises on page A recursive rule tells how consecutive values geoemtric a sequence are 11.33. Sequences and Series Suppose you were looking at the following sequence:.

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Again, you don’t know the value of a n.

After you find a napply the formula,to find the indicated sum. In other words, the value of any term in a sequence can be found by adding the common difference, d, to geomefric preceding term. After substituting for terms you know, write the equation in standard form, factor and solve for n.

Chapter 11 : Sequences and Series : Infinite Geometric Series

In this case you find the value of a term in a sequence by multiplying the preceding term by the common ratio, r. A recursive rule tells how consecutive values of a sequence are related. You can tell if a sequence is geometric if the ratio between all pairs of consecutive terms,is constant. While checking to see if the sequence is arithmetic, you notice that the difference between consecutive terms keeps increasing by one.

You can tell if a sequence is arithmetic if the difference between all pairs of consecutive terms, a n – a n – 1is constant. Finally, try to find a relationship between the previous value, a n – 1and the term number, n. Recall that a 1 represents the first term of the series, n represents the number of terms in the series, and d represents the difference between terms.