The population of a local species of beetle can be found using an infinite geometric series where a1 = 880 and the common ratio is one fourth. write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

the summation of 880 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is divergent

the summation of 880 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is 1,173

the summation of 880 times one fourth to the i power, from i equals 1 to infinity. ; the series is divergent

the summation of 880 times one fourth to the i power, from i equals 1 to infinity. ; the sum is 1,173

Second Option

"the summation of 880 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is 1,173"

Step-by-step explanation:

We know that infinite geometrical series have the following form:

Where is the first term of the sequence and "r" is common ratio

In this case

So the series is:

By definition if we have a geometric series of the form

Then the series converges to     if

In this case and  then the series converges to

Finally the answer is the second option

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: