(1 poni) 1. Consider the sequence 11, 13, 15, 17, 19, 21... Compute the differen

Question

(1 poni) 1. Consider the sequence 11, 13, 15, 17, 19, 21... Compute the difference between successive terms and enter your answer as a list. (For example, if the sequence were 2, 5, 9, you would enter the comma separated list 3, 4 since 5-2-3 and 9-5-4) The sequence of successive differences is suggests that the original sequence (is/is not? ygrowing linearly. 2. Consider the sequence 11, 13, 15, 17, 19, 21... Compute the ratio between successive terms and enter your answer as a list. (For example, if the sequence were 2, 5, 9, you would enter the comma separated list 5/2, 9/5). The sequence of successive differences is suggests ? that the original sequence (isis not) growing exponentially 3. Find a closed formula for the sequence 11, 13, 15, 17, 19, 21... Use n as your index and start with n 0, that is, bo-11. bn 4. Find a closed formula for the sequence -11, 13, -15, 17, -19, 21... Use n as your index and start with n 0, that is, q) =-11.

Explanation / Answer

1. 11, 13, 15,17,19,21,....

difference

13-11=2, 15-13=2, 17-15=2, 19-17=2, 21-19=2

The sequence of successive differences is same, which suggest the origional sequence is growing linearly

2. ratio= 13/11=1.182, 15/13=1.154, 17/13=1.133, 19/17=1.12, 21/19=1.11

The sequence of successive ratio is different, which suggest the origional sequence is not growing exponentially

3. 11,13,15,17,19,21,...

First term b=11

Common difference=2

bn=b +(n-1)d

bn=11+(n-1)2 = 2n+ 9

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