See attachment for your answer:
The 14th term is equal to -44.
y = 12 - 5x
The sequence can be represented by this function.
Each term is being subtracted by 5.
Using this function we can find the 14th time.
y = 12 - 5(14)
y = 12 - 56
y = -44
So you would do,
18 gallons of water divided by 0.5 gallons of water
if you did that correctly you should have gotten... 36 jugs
Answer:
see below
Step-by-step explanation:
The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...
sum = a1/(1 -r)
Applying this to the given series, we get ...
a. sum = 5/(1 -3/4) = 5/(1/4) = 20
b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)
_____
The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...
S -rS = a1
S = a1/(1 -r)
