1. Given the below sequence: -1, -3, -5, -7, . . . (a) What are the next 3 terms? (b) Is this an arithmetic or geometric sequence? (c) Why? (d) What is the 27th term? (Show how to find it and tell me what the 27th term is.)

(a) To find the next three terms , we must firs check if it is arithmetic sequence or a geometric sequence . For it to be an arithmetic sequence , there must be a common difference :

check :

-3 - (-1) = -5 - (-3) = -7 - (-5) = -2

This means that there is a common difference of -2 , which means it is an arithmetic sequence.

The next 3 terms we are to find are: 5th term , 6th term and 7th term.

[tex]t_{5}[/tex] = a + 4d

[tex]t_{5}[/tex] = - 1 + 4 ( -2 )

[tex]t_{5}[/tex] = -1 - 8

[tex]t_{5}[/tex] = - 9

6th term = a +5d

[tex]t_{6}[/tex] = -1 + 5(-2)

[tex]t_{6}[/tex] = -1 - 10

[tex]t_{6}[/tex] = - 11

[tex]t_{7}[/tex] = a + 6d

[tex]t_{7}[/tex] = -1 + 6 (-2)

[tex]t_{7}[/tex] = -1 - 12

[tex]t_{7}[/tex] = -13

Therefore : the next 3 terms are : -9 , -11 , - 13

(b) it is an arithmetic sequence because there is a common difference which is -2

(c) Because of the existence of common difference

(d) [tex]t_{27}[/tex] = a + 26d

[tex]t_{27}[/tex] = -1 + 26 ( -2 )

[tex]t_{27}[/tex] = -1 - 52

[tex]t_{27}[/tex] = - 53