1 / 8

11.4 – Arithmetic Series

11.4 – Arithmetic Series. How do I know if it is an arithmetic series?. A series is the expression for the sum of the terms of a sequence , not just “what is the next terms.

shina
Download Presentation

11.4 – Arithmetic 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. 11.4 – Arithmetic Series

  2. How do I know if it is an arithmetic series? • A series is the expression for the sum of the terms of a sequence, not just “what is the next terms This is a list of the numbers in the pattern an not a sum. It is a sequence. Note it goes on forever, so we say it is an infinite sequence. Ex: 6, 9, 12, 15, 18 . . . Here we are adding the values. We call this a series. Because it does not go on forever, we say it is a finite series. Ex: 6 + 9 + 12 + 15 + 18 Note: if the numbers go on forever, it is infinite; if it has a definitive ending it is finite.

  3. Evaluating a Series • Simply add up the values. Ex: 2, 11, 20, 29, 38, 47 2+11+20+29+38+47 = 147 Easy Cheesy! But isn’t there a quicker way to do this???

  4. Sum of a Finite Arithmetic Series Where: Sn is the sum of all the terms n = number of terms a1 = first term an = last term From our last example: 2+11+20+29+38+47 = 147 147 Let’s try one: evaluate the series: 5, 9, 13,17,21,25,29

  5. Summation When we don’t want to write out a whole bunch of numbers in the series, the summation symbol is used when writing a series. The limits are the greatest and least values of n. Upper Limit (greatest value of n) Explicit function for the sequence Summation symbol Lower Limit (least value of n) So, the way this works is plug in n=1 to the equation and continue through n=3. (5*1 + 1) + (5*2 +1) + (5*3 + 1) = 33

  6. Writing a series in summation form • Ex: 102 + 104 + 106 + 108 + 110 + 112 n = 6 terms 1st term = 1 Rule: Hmmmm. . . . Rule = 100 + 2n Yes, you can add manually. But let’s try using the shortcut: Let’s Evaluate:

  7. Let’s try some Find the number of terms, the first term and the last term. Then evaluate the series:

  8. Let’s try some Find the number of terms, the first term and the last term. Then evaluate the series: Why is the answer not 58? Note: this is NOT an arithmetic series. You can NOT use the shortcut; you have to manually crunch out all the values. N = 10 1st = 1 Last = 10 a1= 1-3 = -2 a10 = 10-3 = 7 N = 4 1st = 2 Last = 5 4+9+16+25 = 54 Notice we can use the shortcut here:

More Related