Daniel invests $10,000 in a savings account that pays 1.5% simple interest. How much will be in the

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

Please help with this question

lisov135 [29]

(x-12)(x-12) would factor to x²-24x+144.

(x-12)(x+12) = x²+144

Option C is correct :)

4 0

3 years ago

Read 2 more answers

I’m trying to find this I have an answer but I don’t know if it’s right 10points

Zolol [24]

Aint it 150 decimeters?

4 0

3 years ago

Combine the like terms to create an equivalent expression:<br>-3z- z

VARVARA [1.3K]

Answer: -4z

Step-by-step explanation:

If you subtract -3 by one, these negatives add up to be -4, making it -4z.

5 0

3 years ago

Define cultural identity in your own words

Semenov [28]

Simply put, cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.

<h3>What is Cultural Identity?</h3>

Cultural identity can be defined as the self-perception of an individual which gives them a sense of belonging to an identical group that shares same qualities which may included music, food, traditions, social class, beliefs, ethnicity, among others.

In summary, we can say that cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.

Learn more about cultural identity on:

brainly.com/question/25729774

#SPJ1

4 0

2 years ago