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FinnZ [79.3K]
3 years ago
11

What is the sum of a 7-term geometric series if the first term is -6, the last term is -24,576, and the common ratio is 4?

Mathematics
2 answers:
Zolol [24]3 years ago
7 0

Answer:  The required sum of the given geometric series is - 32766.

Step-by-step explanation:  We are given to find the sum of a 7-term geometric series if the first term is -6, the last term is -24,576 and the common ratio is 4.

We know that,

if 'a' is the first term and 'r' is the common ratio of a geometric series, then its sum up to n terms is given by

S_n=\dfrac{a(1-r^n)}{1-r},~r1.

In the given geometric series,

first term, a = -6  and  common ratio, r = 4.

Since r = 4 > 1, so the sum up to 7 terms is

S_7\\\\\\=\dfrac{a(r^7-1)}{r-1}\\\\\\=\dfrac{-6(4^7-1)}{4-1}\\\\\\=\dfrac{-6(16384-1)}{3}\\\\\\=-2\times 16383\\\\=-32766.

Thus, the required sum of the given geometric series is - 32766.

Zanzabum3 years ago
3 0
<h3><u>Answer:</u></h3>

Hence, the sum of a 7-term geometric series is:

-32766.

<h3><u>Step-by-step explanation:</u></h3>

We have to find the sum of a 7-term geometric series (i.e. n=7) if the first term(a) is -6, the last term is -24,576, and the common ratio(r) is 4.

We know that the sum of the 7-term geometric series is given as:

S_n=a\times (\dfrac{r^n-1}{r-1})

On putting the value of a,n and r in the given formula we have:

S_7=(-6)\times (\dfrac{4^7-1}{4-1})\\\\\\S_7=-32766

Hence, the sum of a 7-term geometric series is:

-32766.

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Becki put some stamps into her stamp collection book she put 14 stamps on each page if she completely filled 16 pages how many s
aleksandrvk [35]

Answer:

224 stamps.

Step-by-step explanation:

We have been given that Becki put 14 stamps on each page.

To find the total number of stamps that Becki put in the book we will multiply the number of stamps put on each page by the number of completely filled pages.

\text{The total number of stamps in the book}=14\times 16

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7 0
3 years ago
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Agata [3.3K]

Answer:

It's the first option.

Step-by-step explanation:

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Multiplying by 3 to give 3 cos(x -  π/2)  stretches the graph 3 units parallel to the y-axis and adding 3 to this moves the graph up 3 units.

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3 0
3 years ago
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Answer:

1) ven diagram #1

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Step-by-step explanation:

1) lets make a ratio table:

(look at image below, sorry for the horrible writing)

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3 0
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Answer:

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Step-by-step explanation:

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

−9/4 ÷ −11/2

Applying the fractions formula for division,

=−9×2 divided by 4×−11

=−18/−44

Simplifying -18/-44, the answer is

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8 0
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(2n-9)-(-2.4n+4)Find the difference.
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Answer:

The difference is 4.4n−13.

Step-by-step explanation:

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