Question

Write a formula for the general term (the nth term) of the geometric sequence. 1/2 -1/10 1/50 -1/250

Answer 1

@phi @welshfella

Answer 2

A.

an = 1/2(n-1)3/5

B.

an = 1/2 - 1/5(n-1)

C.

an = (1/2)(-1/5)(n-1)

D.

an = (1/5)(-1/2)(n-1)

Answer 3

any idea how to "get" from 1/2 to -1/10 ?
what do you multiply 1/2 by to get -1/10 ?

Answer 4

5 maybe

Answer 5

right track. but you can do better
\[ \frac{1}{2} \cdot x =- \frac{1}{10} \]

Answer 6

if you multiply by 5 you get \[ \frac{5}{2} \]
not what we want

Answer 7

1/5

Answer 8

if you can't see it, try multiplying both sides by 2
and "solve for x"

1/5 is pretty good, but not quite
\[ \frac{1}{2} \cdot \frac{1}{5}= \frac{1}{10} \]
but we want \[ - \frac{1}{10} \]

Answer 9

so -1/5

Answer 10

ok, and to make sure
take the 2nd term in the series
-1/10 and multiply by -1/5
what do we get ?

Answer 11

1/15

Answer 12

i think

Answer 13

multiply top times top and bottom times bottom

Answer 14

ok so 1/50

Answer 15

and if we multiply 1/50 by -1/5 we get -1/250

notice we are getting the original series
1/2 -1/10 1/50 -1/250

Answer 16

yes

Answer 17

here is what we know
\[ \frac{1}{2} \\
\frac{1}{2}\left(-\frac{1}{5}\right)^1 \\
\frac{1}{2}\left(-\frac{1}{5}\right)^2
\]
and so on

Answer 18

yes

Answer 19

if we label the first term as "term number 1"
and the 2nd 2
and then 3
etc
notice each term has 1/2 times (-1/5) to a power one less than the term's number

Answer 20

yes that makes sence

Answer 21

only one of the choices is "short-hand" for that

Answer 22

c

Answer 23

yes

Answer 24

yeah thnx again freind