Question

SEQUENCES QUESTIONS
algebra 2 study guide help
1. what is the 17th term of the sequence that begins -3, 9, -27, 81...?

2. the fifth term of a geometric sequence is 120, and the seventh term is 30. What are the possible values of the sixth term of the sequence?

Answer 1

1. this is a geometric sequence
a1, a1r , a1r^2, a1r^3 ....

where a1 is the first term and r = common ratio

the common ratio can be found by dividing the second term by the first
so for this sequence r = 9 / -3 = -3

Answer 2

the formula for the nth term is

a1(r)^(n-1)

so for the 17th term of this sequence
a1 = -3, n = 17 and r = -3

Answer 3

im a little confused as to what you mean there @welshfella

Answer 4

are you talking about my last post?

Answer 5

yes, if i plug it all in i should have -3(-3)^(17-1) right?

Answer 6

yes

Answer 7

im not sure if that computed correct because i got -129140163

Answer 8

you'll need to use your calculator of course!

Answer 9

yes Thats right

Answer 10

i did, i put in what i typed and got that long answer

Answer 11

alrighty, thanks! can you help me work out the next one?

Answer 12

yes thats correct
these GP terms with a common ratio greater than 1 quickly get massive

Answer 13

seventh term = a1*r^6
fifth term = a1*r^4


dividing a1*r^6 / a1*r^4 = r^2 = 30/120

so r^2 = 1/4

and r = ?

Answer 14

what are the 2 square roots of 1/4?

Answer 15

im sorry, this one is confusing me a bit give me a sec

Answer 16

i don't know

Answer 17

sqrt 1/4 is 1/2 or -1/2

so the common ratio r = 1/2 or -1/2

to get the next term in the series you multiply by this value of r

so as the 5th term is 120 the 6th term will be either
120 * 1/2 or 120 * -1/2

Answer 18

oh okay, that makes a little more since.
so 120*1/2 and 120*-1/2 are my possible values for the sixth term, correct?

Answer 19

yes

Answer 20

perhaps i confused you a little with the formulas

Answer 21

the sequence would be either

120 , 60 ,30
or 120,-60,30

Answer 22

i must go right now

Answer 23

okay! thanks!