# Math

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The height of a plant after each of the first three weeks was 7mm, 20mm, and 33mm, respectively. If this pattern of growth continues, in what week will the plant be more than 100mm tall?

The answer is 9 weeks.

This is what I did, and it's clearly wrong:
tn = 7 + (n-1)13
tn = 7 + 13n - 13
tn = 13n - 6

100 = 13n - 6
100 + 6 = 13n
106/13 = n
I get a crazy decimal (8.1538....) which shouldn't be the answer...

What am I doing wrong, and how do you properly answer this question?

Thanks very much in advance!

• Math -

You did just fine

it said "more than 100 mm"

so
13n - 6 > 100
13n >106
n > 106/13 or > 8.15..

So you would answer...
" the plant would be more than 100 mm in the 9th week"

check:
week 8 = t8 = a+7d = 7+7(13) = 98 , less than 100
week 9 = t9 = a+8d = 7+8(13) = 111 , more than 100

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