MTE 210: Section 1-2

List the next three terms to continue a pattern. a. 5, 6, 14, 32, 64, 115, 191

5, 6 ,14, 32, 64, 115, 191 1.) Differences: 2.) Differences again: 1, 8, 18, 32, 51, 76 7, 10, 14, 19, 25 3.) Differences again: 3.) Differences again: 3, 4, 5, 6 1, 1, 1, 1 So to get the next term in your sequence, work your way back up, extending the last row by 1, then going up insert 7, then above that 25+7=32, then 76+32=108, then 191+108=299 The next s terms are 299, 447, 644.

The arithmetic avg of 2 #s x & y is x+y/2. Use deductive reasoning to explain why b is the average.

B is the arithmetic avg bc if b were on a # line, it would be the average of the number before and after it.

A student claims that she has found an easy way to find the number of terms in an arithmetic sequence: '' You take the diff bt the last & first terms & divide by the common difference. How do you respond?

She is almost there. She needs to add 1 to her answer she gets using the equation she gave bc you have to count the first term...

Joey said that 4, 24, 44, and 64 all have remainder 0 when divided by 4, so all numbers that end in 4 must have a 0 remainder when divided by 4. How do you respond?

That is not true bc if 34 is divided by 4, you get a remainder.

Al & Bety were asked to extend the sequence 2, 4, 8,... Al said his answer of 2, 4, 8, 16, 32, 64 was right. Betty said Al was wrong and it should be 2, 4, 8, 14, 22, 32, 44. What do you tell these students?

They are both right....

How many terms is there in this sequence? 9, 13, 17, 21, 25, ...., 353

Use hop method 100

If a fixed # is added to each term of an arithmetic sequence, is the resulting sequence an arithmetic sequence?

Yes; adding a fixed # would just increase the difference between the numbers

If each term of an arithmetic sequence is multiplied by a fixed number, is the resulting an arithmetic sequence?

Yes; again it would just increase the difference between the numbers

The first windmill has 5 matchstick squares, the second has 9, and the third has 13. How many matchstick squares are in the a. 10th windmill? b. the nth windmill? c. How many matchsticks will it take to build the nth windmill?

a. 4(10) + 1 = 41 b. 4(n) + 1 c. 12(10) + 4 = 124

Assume that the following patterns are built of square tiles and the pattern continues. a. How many square tips are there in the sixth figure? b. How many square tiles are there in the nth figure? c. Is there a figure that has exactly 1259 squares? If so, which one?

a. 41 b. n^2 + n -1 (2^2) + 1 = 5 (3^3) + 2 = 11 c. 34^2 + 33 = 1,189 nope (4^4) + 3 = 19 35^2 + 34 = 1259 (5^5) + 4 = 29 ANSWER: The 35th fig (6^6) + 5 = 41 ANSWER: 41

The fig below shows the first 3 terms of a sequence of shaded figs containing small square tiles. a. How many shaded tiles are there in the nth fig? b. How many white tiles are there in the nth fig?

a. N^2. b. 8 + 4(n - 1)

Find the 100th term and the nth term for the sequences in the last exercise.

b. 50(100) + 20 = 5020 c. 3^100-1 3^99

Each of the following sequences is either arithmetic or geometric. Identify the sequences and list the next three terms for each. b. 70, 120, 170 c. 1, 3, 9

b. arithmetic; 220, 270, 320 c. geometric; 27, 81, 243