Identify whether the series is a convergent or divergent geometric series and find the sum, if possible.
this is a convergent geometric series. the sum cannot be found.
this is a divergent geometric series. the sum cannot be found.
this is a convergent geometric series. the sum is –4.
this is a divergent geometric series. the sum is –4.

Step-by-step explanation:

There is a series given which can be written in expanded form as

16+16(5)+16(5^2)+

16 is a common factor to all

Hence

=16(1+5+5^2+5^3+...+5^n+...)

We find that this is a geometric series with I term =1 and common ratio = 5

Since 5, the common ratio is >1, the infinite series sum will diverge

Hence the series is a geometric series with infinite sum diverging.

Correct answer is:

This is a divergent geometric series. The sum cannot be found.

linear

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."