math

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Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of greater length than the speech she gave the week before. The table below show the length of several of her speeches:

WK #/Length of Speech (seconds)
3/150, 4/180, 5/210, 6/240

If this trend continues, in which week will she give a 12-minute speech?

Choices are:
22
12
15
24

By converting 12 minutes to 720 seconds and going week by week, I chose 22.

How do I set this up as a problem and solve it? Thanks

• math -

each week she increases her speech by 30 seconds
12 minutes = 720 seconds
(you are right so far)

This is an arithmetic sequence, where
a = 150 , d = 30
we need to find which term is 720
150 + (n-1)(30) = 720
30n - 30 = 570
30n = 600
n = 20

but what I considered first term is really the third term (3rd week)
so she reaches the 12 minute speech in week 22

You are right!

• math -

• math -

the correct answer is actually Alyssa is a satanist and she will die before the last speech which is 12 minutes...

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