3 years ago

It took Madge 45 minutes to get to school after she woke up. If she arrived at school at 8:35, what time did she wake up?

Mathematics

2 answers:

g100num [7]3 years ago

6 0

Answer: Madge woke up at 7:50.

Step-by-step explanation:

You can subtract the 8:35 minus 45 minutes to get 7:50

Karolina [17]3 years ago

3 0

She woke up at 7:50.
explanation:
8:35-:45=7:50

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If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16 then what is the fourteenth term?

Agata [3.3K]

<h3>Given</h3>

A geometric sequence such that ...

$a_2=-2\quad\text{and}\quad a_5=16$

$a_{14}$

<h3>Solution</h3>

We can use the ratio of the given terms to find the common ratio of the sequence, then use that to find the desired term from one of the given terms. We don't actually need the common ratio (-2). All we need is its cube (-8).

$a_2=a_1r^{(2-1)}=a_1r^1\\a_5=a_1r^{(5-1)}=a_1r^4\\a_{14}=a_1r^{(14-1)}=a_1r^13=a_5r^9\\\\\dfrac{a_5}{a_2}=\dfrac{a_1r^4}{a_1r^1}=r^3=\dfrac{16}{-2}=-8\\\\r^9=\left(r^3\right)^3=(-8)^3=-512\\a_{14}=a_5(-512)\\\\a_{14}=-8192$