Question

Negative 2 and two-thirds, negative 5 and one-third, negative 10 and two-thirds, negative 21 and one-third, negative 42 and two-thirds, ellipsis
Which formula can be used to describe the sequence?

f(x 1) = –2f(x)
f(x 1) = Negative one-halff(x)
f(x 1) = One-halff(x)
f(x 1) = 2f(x)

Answer 1

-2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3...

the mixed fractions make the pattern hard to see at first. convert mixed fractions to improper fractions.

as a reminder: to convert a mixed # to a fraction, multiply the denominator * the whole number, add the numerator, then write it over the denominator. since we're dealing with negative signs, I would recommend dropping the negative sign during the conversion, then put the negative sign back at the end.

ex:
\[2 \frac{ 2 }{ 3 } \rightarrow(3)(2)+2\rightarrow8\rightarrow \frac{ 8 }{ 3 }\]

so \[2\frac{ 2 }{ 3 }=\frac{ 8 }{ 3 }\]
and by extension
\[-2\frac{ 2 }{ 3 }=-\frac{ 8 }{ 3 }\]

repeat this process with the next one or two numbers from the sequence (just enough to see the pattern). all of the terms should have the same denominator, so you really just need to look at the common ratio between the numerators.