Answer:
S = 8
Step-by-step explanation:
An infinite geometric series is defined as limit of partial sum of geometric sequences. Therefore, to find the infinite sum, we have to find the partial sum first then input limit approaches infinity.
However, fortunately, the infinite geometric series has already set up for you. It’s got the formula for itself which is:

We can also write in summation notation rather S-term as:

Keep in mind that these only work for when |r| < 1 or else it will diverge.
Also, how fortunately, the given summation fits the formula pattern so we do not have to do anything but simply apply the formula in.

Therefore, the sum will converge to 8.
Please let me know if you have any questions!
Answer:
40 minutes.
Step-by-step explanation:
- time spent on the thread mill as a function of d(day) = t(d)
= 30 +2(d-1) minutes
[where d represents day number]
(when d is 1 the time spent should be 30
so substitute d=1 and check it will be 30 only.
on first day he will spend 30 minutes so, I added 30 .
and on every additional day( these additional days are excluding first day), he will increase the time by 2 minutes.so, I added 2(d-1) to initial 30 minutes)
- so, T(6), the minutes he will spend on the treadmill on day 6=
=30+2(6-1)
=30+2(5)
=30+10
=40 minutes
We know, opposite sides are parallelogram is parallel, therefore slopes are equal.
Slope of line one :

So, equation of other line passing through (-4,5) and have slope of -0.5 is :
y-5 = -0.5( x-(-4))
y-5 = -0.5x - 2
y + 1/2x = 3
2y + x = 6
Therefore, equation of line containing the (-4, 5) is 2y + x = 6.
Hence, this is the required solution.