M3L2
- 1. M3L2 ARITHMETIC SEQUENCES & SERIES By M Willatt Pictures and summation made on Microsoft Word
- 2. We’re going to work with these 4 arithmetic sequences in order to practice the steps you need to be able to do for M3L2! Study them for a minute before you jump in… 1. -5, -7, -9, -11, -13, … 2. The first term is 2 and the fifth term is 70. 3. 0, 1.5, 3, 4.5, 6, … 4. The first term is 11 and the third term is -3.
- 3. Find the common difference for each arithmetic sequence: 1. -5, -7, -9, -11, -13, … d = term – preceding term = (-7) – (-5) = - 2 2. The first term is 2 and the fifth term is 70. d = difference between terms = 70-2 = 68 = 17 difference in term #’s 5-1 4 3. 0, 1.5, 3, 4.5, 6, … d = term – preceding term = 1.5 – 0 = 1.5 4. The first term is 11 and the third term is -3. d = difference between terms = -3 -11 = -14 = -7 difference in term #’s 3-1 2
- 4. Reminder on how to write the explicit form of an…
- 5. Write the explicit formula for each using the d we just found: 1. -5, -7, -9, -11, -13, … a1= -5 & d = -2 an= -5 + (n-1)(-2) 2. The first term is 2 and the fifth term is 70. a1= 2 & d = 17 an= 2 + (n-1)17 3. 0, 1.5, 3, 4.5, 6, … a1= 0 & d = 1.5 an= 0 + (n-1)1.5 4. The first term is 11 and the third term is -3. a1= 11 & d = -7 an= 11 + (n-1)(-7)
- 6. Find the 13th term using the explicit formula we just found: 1. an= -5 + (n-1)(-2) a13= -5 + (13-1)(-2)= -5 +(12)(-2) = -29 2. an= 2 + (n-1)17 a13= 2 + (13-1)17= 2 +(12)17 = 206 3. an= 0 + (n-1)1.5 a13= 0 + (13-1)1.5= 0 +(12)1.5 = 18 4. an= 11 + (n-1)(-7) a13= 11 + (13-1)(-7)= 11 +(12)(-7) =-73
- 7. Remember a series is the sum of the terms in a sequence. To add up the 1st “n” terms, we could write: But what if “n” was 50? You would have to find the first 50 terms & then add them. That’s a lot of work…
- 8. Fortunately, there is a formula that only requires the 1st & last term of the series:
- 9. Find the sum of the first 13 terms: 1. a1= -5 a13= -29 𝑆13 = 13 2 −5 + −29 = -221 2. a1= 2 a13= 206 𝑆13 = 13 2 2 + 206 = 1352 3. a1= 0 a13= 18 𝑆13 = 13 2 0 + 18 = 117 4. a1= 11 a13= -73 𝑆13 = 13 2 11 + −73 = -403
- 10. • If you’re asked for the common difference, see what number is being added between each term. You can subtract 2nd term – 1st term OR 3rd term – 2nd term, etc. • If you’re asked for the 50th term, you need to substitute a 50 into the explicit formula for n. If you don’t have the formula, then write it using a1 and d. • If you’re asked to find the partial series, you can use the formula Sn. However, you may need to find the term an first using the explicit formula.