Download to read offline
More Related Content
Similar to 2-Arithmetic Sequence grade 10 mathematics.pptx
More from NatanielSantos15
2-Arithmetic Sequence grade 10 mathematics.pptx
- 1. Arithmetic Sequence Determines arithmeticmeans, nth term of an arithmetic sequence and sum of the terms of a given arithmetic sequence. (M10AL-Ib-1) NATANIEL B. SANTOS JR.
- 2. What is ARITHMETICSEQUENCE • A sequence is a function whose domain is the finite set {1, 2, 3,…, n} or the infinite set {1, 2, 3,… }. • An arithmetic sequence is a sequence where every term after the first is obtained by adding a constant called the common difference. Example: 1, 4, 7, 10, 13 finite 15, 11, 7, 3, -1, … infinite
- 3. Arithmetic Sequence 1. 1,4, 7, 10, 13, … 2. -3, -7, -11, -15, -19, … 3. 1, 2, 4, 8, 16, 32, … 4. -81, -27, -9, -3, -1 5. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … 3 -4
- 4. Seatwork #102: WriteARITHMETIC if the following are arithmetic sequence and NOT ARITHMETIC if otherwise on the space provided. ____1. 18, 24, 30, 36, 42 ____6. -160, -80, -40, -20, -10, -5 ____2. 3, 6, 12, 24, 48, 96, … ____7. 15, 30, 45, 60, 75, … ____3. -5, -15, -45, -135, -405 ____8. -25, 20, -15, 10, - 5 ____4. -59, -50, -41, -32, -23, … ____9. ____5. 1, 3, 7, 15, 31, … ____10. …
- 5. Next term/s ofArithmetic Sequence. • 1. 2, 8, 14, __, __, __ • 2. __, 4, 12, 20, __ • 3. 27, 20, __, __, -1 • 4. __, __, __, 11, 15, 19 • 5. 19, __, __, __, -17, -26 20 26 32 -4 28 13 6 -1 10 1 -8 3 7
- 6. Seatwork# 103 • 1.)3, 12, 21, __, __, __ 6.) 17, 14, __, __, 5 • 2.) 8, 3, -2, __, __ 7.) 4, __, __, 19, 24 • 3.) 5, 12, __, 26, __ 8.) __, __, __, 8, 12, 16 • 4.) 2, __, 20, 29, __ 9.) -1, __, __, __, 31, 39 • 5.) __, 4, 10, 16, __ 10.) 13, __, __, __, -11, -17
- 7. 1. What isthe 10th term in the arithmetic sequence 5, 12, 19, 26, … ? • 5, 12, 19, 26, 33, 40, 47, 54, 61, 68 • How about the 20th term? • How about the 105th term? • How about the 1000th term? 1st 2nd 7th 8th 9th 10th 4th 5th 6th 3rd
- 8.
- 9. Formula: How to solvefor common difference? • Subtract and
- 10. Example: 1. What isthe 10 term in the arithmetic sequence 5, 12, 19, 26, … ? • n = 10
- 11.
- 12. Seatwork # 104:Answer each of the following. 1. What is the 8th term in the arithmetic sequence -5, -7, -9, -11, …? 2. What is the 13th term in the arithmetic sequence 82, 73, 64, 55, 46, … ? 3. What is the 28th term in the arithmetic sequence 1, 14, 27, 40, 53, 66, … ? 4. What is the 50th term in the arithmetic sequence -99, -94, -89, -84, -79, … ? 5. What is the 102nd term in the arithmetic sequence – 10, -20, -30, -40, … ?
- 13. If the 5thterm of an arithmetic sequence is 23 and the common difference is 4, what is the 10th term? • 23 • n = 5
- 14. If the 5thterm of an arithmetic sequence is 23 and the common difference is 4, what is the 10th term? • 23 • 23 • 23 • 23-16
- 15. If the 5thterm of an arithmetic sequence is 23 and the common difference is 4, what is the 10th term? • n = 10
- 16. If the 5thterm of an arithmetic sequence is 23 and the common difference is 4, what is the 10th term?
- 17. More examples: • 1.If the 9th term of an arithmetic sequence is 20 and the common difference is -5, what is the 18th term? • 2. If the 7th term of an arithmetic sequence is -28 and the common difference is 4, what is the 23rd term?
- 18. Seatwork # 105 1.If the 4th term of an arithmetic sequence is -10 and the common difference is -2, what is the 11th term? 2. If the 6th term of an arithmetic sequence is 70 and the common difference is -5, what is the 20th term? 3. If the 5ht term od an arithmetic sequence is -4 and the common difference is 11, what is the 32nd term?
- 19. Arithmetic Means arethe terms between any two nonconsecutive terms of an arithmetic sequence. • Insert 4 arithmetic means between 5 and 25. • Since we are required to insert 4 terms, then there will be 6 terms in all. • 5, ___, ___, ___, ___, 25
- 20. Arithmetic Means arethe terms between any two nonconsecutive terms of an arithmetic sequence. • Common difference:
- 21. Arithmetic Means arethe terms between any two nonconsecutive terms of an arithmetic sequence. • 25 • 25 • 25 • 20 • 4
- 22. Arithmetic Means arethe terms between any two nonconsecutive terms of an arithmetic sequence. • 5, ___, ___, ___, ___, 25 • 5+4=9 9+4=13 • 13+4=17 17+4=21 9 13 17 21
- 23. More examples: 1. Insert5 arithmetic means between 2 and 38. 2. Insert 3 arithmetic means between -55 and -11 3. Insert 8 arithmetic means between -6 and -51
- 24. Seatwork #106: Solvefor the arithmetic means in each of the following. 1. Insert 4 arithmetic means between 7 and 27 2. Insert 5 arithmetic means between 62 and 8 3. Insert 7 arithmetic means between -100 and -20 4. Insert 10 arithmetic means between -9 and -42 5. Insert 8 arithmetic means between 32 and -13
- 25. What is thesum of the first 10 terms in 8, 12, 16, 20, 24, … ? • 8, 12, 16, 20, 24, ___, ___, ___, ___, ___, • =8+12+16+20+24+28+32+36+40+44 • =260 • What about first 15 terms? • What about first 100 terms? • What about first 3000 terms? 28 32 36 40 44
- 26.
- 27. Find the sumof the first 10 terms of the arithmetic sequence 5, 9, 13, 17, ...
- 28. More Examples: 1. Findthe sum of the first 20 terms of the arithmetic sequence -2, -5, -8, -11, … 2. What is the sum of the first 15 terms in the arithmetic sequence 7, 13, 19, 25, 31, …? 3. Find the sum of the first 18 terms of the arithmetic sequence 78, 69, 60, 51, 42, …?
- 29. Seatwork #107: Findthe sum of terms in each of the following. 1. Find the sum of the first 10 terms of the arithmetic sequence 15, 22, 29, 36, … 2. What is the sum of the first 15 terms in the arithmetic sequence -3,-11,-19, -27, -35, …? 3. Find the sum of the first 20 terms of the arithmetic sequence -85, -74, -63, -52, -41, …? 4. Find the sum of the first 18 terms of the arithmetic sequence -3, -13, -23, -33, -43, …? 5. What is the sum of the first 27 terms in the arithmetic sequence 103, 95, 87, 79, 71, …?