Question

Identify the 17th term of a geometric sequence where a1 = 16 and a5 = 150.06. Round the common ratio and 17th term to the nearest hundredth. someone answer please

Answer 1

the n-th term of a geometric sequence is\[a_n = a_1 r^{n-1}\]use that equation to find the common ratio (r) and the 17th term (a17)

Answer 2

im getting stuck at solving for r

Answer 3

that parts just algebra:\[\frac{a_n}{a_1}=r^{n-1}\]
\[\large \sqrt[{n-1}]{\frac{a_n}{a_1}}=r\]

Answer 4

4 \[\sqrt{150.06}\] /16 = r ?

Answer 5

yes, if i read that right :)

lets use exponents instead :)\[\sqrt[a]{b}=b^{1/a}\]

\[(\frac{150.06}{16})^{1/4}\]

Answer 6

whenever i divide 150.06 by 16, i get 9.37875 or 9,.38 i just dont know how to ger rid of the 4 in front of the square root sign

Answer 7

wait how do you get rid of the 1/4 ?

Answer 8

you dont get rid of it, you use it

Answer 9

well how do you use a fraction exponent ?

Answer 10

are you doing this by hand, calculator, or website assisted?

Answer 11

hand and calculator

Answer 12

by hand is almost impossible

do you know where the exponent buttom on your calc is? should look like "^"

Answer 13

other buttons you need are "(" "/" and ")"

Answer 14

when i plug it in to mu calculator i get 2.3446875

Answer 15

or 2.34

Answer 16

ill use google to verify :)

http://www.google.com/search?rlz=1C1CHFX_enUS482US482&sourceid=chrome&ie=UTF-8&q=(150.06%2F16)%5E(1%2F4)

1.74999...

Answer 17

so r is 1.74999 ? or 1.75 ?

Answer 18

round as it tells you to round, but yes

Answer 19

so then i plug back into orignial equation ?

Answer 20

well, that is why we wanted it to begin with, so that we could use it. so im going to go with a yes

Answer 21

okayy

Answer 22

a17 = 16 r^16 if you need a little guidance ;)

Answer 23

i got the answer thank you