What is 8 divide by 18.88?

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

$\displaystyle \large{r=\frac{a_{n+1}}{a_n}}$

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

Above should be applied for series that have common ratio not equal to 1.

$\displaystyle \large{S_n=a_1 \cdot n}$

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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7 0

3 years ago

Question 2 of 20

nikklg [1K]

Given:

The function on the Input output table.

To find:

The range of the given function.

Solution:

We know that, range is the set of output values.

From the given table it is clear that, hours of training is the input variable and pay per month is the output value.

So, range of the given function is the set of pay per month.

Range = {1100, 1200, 1300, 1400, 1500, 1600, 1700}

Therefore, the correct option is A.

3 0

3 years ago

Last year the sales at a bookstore were 75% fiction books, and 25% nonfiction books.

natulia [17]

It is 15.25 and i know it is right

8 0

4 years ago

Read 2 more answers

You use a line best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data

Veseljchak [2.6K]

Answer:

You can be reasonably and mostly towards the strong side of that it is close.

The correlation coefficient is a strong negative correlation, meaning it is most likely close.

Step-by-step explanation:

6 0

3 years ago

How do you graph x-y=1 and 3x+2y=-12

Nataliya [291]

Answer:

Graph the equations

Step-by-step explanation:

x - y = 1

3x + 2y = - 12

Rewrite equations into y=mx+b form:

y = -1 + x

y = -6 - 1.5x

Graph it!

3 0

3 years ago