Answer:
see below
Step-by-step explanation:
The terms being summed are of the form ...
a1(r)^(i-1)
which is the form of the general term of a geometric sequence. The summation symbol tells you the values of i range from 1 to 6, so this is the sum of 6 terms of the series. (n=6)
Comparing the form of the general term to the one shown, you can see that the leading coefficient (a1) is -4, and the common ratio (r) is 1/2. With these values in mind, the first and third answer choices are possibilities. However, the sum must be negative, since all of its terms are negative. Thus the only viable answer choice is the third one.
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<em>Check</em>
The sum of n terms of a geometric series is ...
Sn = a1(1 -r^n)/(1 -r)
For the given values, this is ...
S6 = -4(1 -(1/2)^6)/(1 -1/2) = -4(63/64)/(1/2) = -63/8
Answer:
2z-31 = -9z+24
First, combine like terms: 11z = 55
Then, divide both sides by 11: 11z/11 = 55/11
Simplify: z=5
Step-by-step explanation:
Attach the numbers What number
Answer:
B
Step-by-step explanation:
If you use the general equation for an arithmetic sequence,
,
where aₙ is the number of minutes for movie n,
a₁ is the length of the first movie in minutes, and
d is the difference between each movie, in minutes
Our sequence is this:
If we want the length of the second movie (we already know the length of the first), we fill in n with 2:
which gives us a length of 72. Now for the length of movie n = 3:
which gives us a length of 74. Now for the length of movie n = 4:
which gives us a length of 76. One more and I'm sure you'll notice the pattern:
which gives us a length of 78. Now we will find the length of the 14th movie and add up by 2's all the way up to that number of minutes:
which gives up a length of 96 minutes. We will add up by 2's from 70 to 96:
Help you with what because I don't see anything?
