Question

Starts out 6 inches then 9 and by the 2nd day it's 15 inches each day it grows the same amount as the day before and plus another 3 inches what day will it be longer than 11 feet

Answer 1

In 8 days the length will be more than 11 feet.

Explanation:

We are given the following in the question:

Length:

6, (6+3), (6+3+3), (6+3+3+3), ...

We have to find that at what day will it be greater than 11 feet that is 132 inches.

Thus, the growth follows an arithmetic progression such that

First term, a = 6

Common difference, d = 3

The sum is greater than 132.

Sum of n terms is given by:

`S_n = (n)/(2)(2a + (n-1)d)`

Putting values, we get,

`132 > \displaystyle(n)/(2)(12 + (n-1)3)\\\\264 > n(12 + 3n-3)\\\\264 > 9n + 3n^2\\3n^2 + 9n - 264 < 0\\n^2 + 3n-88<0\\(n+ 11)(n - 8)<0\\\Rightarrow n < 8`

Thus, in 8 days the length will be more than 11 feet.