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4 years ago

What is the recursive formula for this geometric sequence with this explicit formula?

Mathematics

2 answers:

prohojiy [21]3 years ago

8 0

Answer: B(APEX)

Step-by-step explanation:

vlada-n [284]3 years ago

6 0

The n th term ( explicit formula) for a geometric sequence is

$a_{n}$ = $a_{1}$ $(r)^{n-1}$

where $a_{1}$ is the first term and r the common ratio, hence

$a_{1}$ = 6 and r = - $\frac{1}{4}$

The recursive formula lets us find the next term in the sequence from the previous term by multiplying the previous term by r, hence

$a_{n}$ = $a_{n-1}$ ( - $\frac{1}{4}$ )with $a_{1}$ = 6

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Find CD if C(0,3) and D(4,7)

weeeeeb [17]

$C(0,3) \\
x_1=0 \\
y_1=3 \\ \\
D(4,7) \\
x_2=4 \\
y_2=7 \\ \\
\overset{\underline{\ \ \ \ }}{CD} =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-0)^2+(7-3)^2}= \\
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3 years ago

Many credit card companies charge a compound interest rate of 1.8% per month on a credit card balance. Nelson owes $850 on a cre

Finger [1]

The sequence will be

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$850, 865.30, 880.875, 896.731, 912.872, ...$

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3 years ago

Read 2 more answers

Explain determination ......??

kolezko [41]

Determination is your will power of doing something. Someone who is determined has the firmness of purpose and the resolve to achieve a goal.

Synonyms:

resolution, resolve, resoluteness, character.

Antonyms:

weak-mindedness, pusillanimity.

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3 years ago

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George is considering two different investment options. The first option offers 7.4% per year simple interest on the

jok3333 [9.3K]

Answer:

Part A: The value of the simple interest investment at the end of three years is $12,220

Part B: The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C: The simple interest investment is better over the first three years

Part D: I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Step-by-step explanation:

Part A:

A = P + P r t, where

A represents the value of the investment
P represents the original amount
r represents the rate in decimal
t represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ First option offers 7.4% per year simple interest

∴ r = 7.4% = 7.4 ÷ 100 = 0.074

∵ He may not withdraw any of the money for three years after

the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴ A = 10,000 + 10,000(0.074)(3)

∴ A = 10,000 + 2,220

∴ A = 12,220

The value of the simple interest investment at the end of three years is $12,220

Part B:

$A=P(1+\frac{r}{n})^{nt}$ , where

A represents the value of the investment
P represents the original amount
r represents the rate in decimal
n is a number of periods of a year
t represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ The second option offers a 6.5% interest rate compounded quarterly

∴ r = 6.5% = 6.5 ÷ 100 = 0.065

∴ n = 4 ⇒ quarterly

∵ He may not withdraw any of the money for three years after

the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴ $A=10,000(1+\frac{0.065}{4})^{(4)(3)}$

∴ $A=10,000(1.01625)^{12}$

∴ A = 12,134.08

The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C:

∵ 12,220 > 12,134.08

∴ The simplest interest investment is better than the compounded

interest investment at the end of three years

The simple interest investment is better over the first three years

Part D:

I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Look to the attached graph below

The red line represents the simple interest investment
The blue curve represents the compounded interest investment
(Each 1 unit in the vertical axis represents $1000)
After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interest
After that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest

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3 years ago

3x to the 2nd power +9x +6 use FOIL

Advocard [28]

The answer if you need it factored is 3(x+2)(x+1)

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3 years ago