Digits. I need help! 29/6 is =

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

2 years ago

Omar wants to purchase a bike helmet for 22.55 and a bike for 134.45.

noname [10]

Answer:

$169.96 dollars

Step-by-step explanation:

Given the following questions:

8.25% of 22.55 and 134.45

In order to find the answer, we will have to add the initial costs of the items together, then we will calculate using the formula for percentages to find the tax rate.

$22.55+134.45=157$
$157$

Calculate the percentage:
 $\frac{p\times c}{100}$
$\frac{8.25\times157}{100} =8.25\times157=1295.25\div100=12.9525$
$=12.9525$
$12.9525$
$2 < 5$
$=12.96$

Add the sales tax:
$157+12.96=169.96$
$=169.96$

Which means the two items along with an 8.25% sales tax costs "$169.96 dollars."

Hope this helps.

5 0

2 years ago

4. Select all the ways that describe the

postnew [5]

Answer:

all

Step-by-step explanation:

have the awnserbbbnnnnnnnnnnnn

4 0

2 years ago

The area between z = 1.74 and z = 1.25 Round your answer to three decimal places.

balu736 [363]

Answer:

The area between z = 1.74 and z = 1.25 is of 0.065.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The area between two values of Z is given by the subtraction of the pvalue of the larger value by the smaller.

The area between z = 1.74 and z = 1.25.

This is the pvalue of z = 1.74 subtracted by the pvalue of z = 1.25.

z = 1.74 has a pvalue of 0.959

z = 1.25 has a pvalue of 0.894

0.959 - 0.894 = 0.065

The area between z = 1.74 and z = 1.25 is of 0.065.

5 0

2 years ago

What is the length of one side of a regular pentagon if the perimeter is 120 cm?

Alina [70]

The answer is D: 5p = 120

6 0

3 years ago

Digits. I need help! 29/6 is = _5/6 ​

Digits. I need help! 29/6 is = _5/6