1 / 17

11.2 Arithmetic Sequences & Series

11.2 Arithmetic Sequences & Series. p.659 What is an arithmetic sequence? What is the rule for an arithmetic sequence? How do you find the rule when given two terms?. Arithmetic Sequence:. The difference between consecutive terms is constant (or the same).

nina-lawrence
Download Presentation

11.2 Arithmetic Sequences & Series

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 11.2 Arithmetic Sequences & Series p.659 What is an arithmetic sequence? What is the rule for an arithmetic sequence? How do you find the rule when given two terms?

  2. Arithmetic Sequence: • The difference between consecutive terms is constant (or the same). • The constant difference is also known as the common difference (d).

  3. -10,-6,-2,0,2,6,10,… -6--10=4 -2--6=4 0--2=2 2-0=2 6-2=4 10-6=4 Not arithmetic (because the differences are not the same) 5,11,17,23,29,… 11-5=6 17-11=6 23-17=6 29-23=6 Arithmetic (commondifference is 6) Example: Decide whether each sequence is arithmetic.

  4. Rule for an Arithmetic Sequence an=a1+(n-1)d

  5. Example: Write a rule for the nth term of the sequence 32,47,62,77,… . Then, find a12. • There is a common difference where d=15, therefore the sequence is arithmetic. • Use an=a1+(n-1)d an=32+(n-1)(15) an=32+15n-15 an=17+15n a12=17+15(12)=197

  6. Example: One term of an arithmetic sequence is a8=50. The common difference is 0.25. Write a rule for the nth term. • Use an=a1+(n-1)d to find the 1st term! a8=a1+(8-1)(.25) 50=a1+(7)(.25) 50=a1+1.75 48.25=a1 * Now, use an=a1+(n-1)d to find the rule. an=48.25+(n-1)(.25) an=48.25+.25n-.25 an=48+.25n

  7. Now graph an=48+.25n. • Just like yesterday, remember to graph the ordered pairs of the form (n,an) • So, graph the points (1,48.25), (2,48.5), (3,48.75), (4,49), etc.

  8. Example: Two terms of an arithmetic sequence are a5=10 and a30=110. Write a rule for the nth term. • Begin by writing 2 equations; one for each term given. a5=a1+(5-1)d OR 10=a1+4d And a30=a1+(30-1)d OR 110=a1+29d • Now use the 2 equations to solve for a1 & d. 10=a1+4d 110=a1+29d (subtract the equations to cancel a1) -100= -25d So, d=4 and a1=-6 (now find the rule) an=a1+(n-1)d an=-6+(n-1)(4) OR an=-10+4n

  9. Example (part 2): using the rule an=-10+4n, write the value of n for which an=-2. -2=-10+4n 8=4n 2=n

  10. What is an arithmetic sequence? The difference between consecutive terms is a constant • What is the rule for an arithmetic sequence? an=a1+(n-1)d • How do you find the rule when given two terms? Write two equations with two unknowns and use linear combination to solve for the variables.

  11. Assignment p. 663, 15-43 odd

  12. Arithmetic Sequences and Seriesday 3 What is the formula for find the sum of a finite arithmetic series?

  13. Arithmetic Series • The sum of the terms in an arithmetic sequence • The formula to find the sum of a finite arithmetic series is: Last Term 1st Term # of terms

  14. Find the sum of the 1st 25 terms. First find the rule for the nth term. an=22-2n So, a25 = -28 (last term) Find n such that Sn=-760 Example: Consider the arithmetic series 20+18+16+14+… .

  15. -1520=n(20+22-2n) -1520=-2n2+42n 2n2-42n-1520=0 n2-21n-760=0 (n-40)(n+19)=0 n=40 or n=-19 Always choose the positive solution!

  16. What is the formula for find the sum of a finite arithmetic series?

  17. Assignment: p. 663 45-56 all Skip 49 & 50

More Related