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laila [671]
1 year ago
5

The sum of an infinite geometric series is $27$ times the series that results if the first three terms of the original series ar

e removed. What is the value of the series' common ratio
Mathematics
1 answer:
SVEN [57.7K]1 year ago
8 0

Let a be the first term in the series and r the common ratio. Then the infinite series converges to

a + ar + ar^2 + ar^3 + ar^4 + ar^5 + \cdots = \dfrac a{1-r}

Removing the first three terms from the left side effectively multiplies the right side by 27, so

ar^3 + ar^4 + ar^5 + \cdots = \dfrac{27a}{1-r}

By elimination,

a + ar + ar^2 = -\dfrac{26a}{1-r}

Solve for r. We can eliminate a so that

1 + r + r^2 = -\dfrac{26}{1-r} \\\\ \implies 1-r^3 = -26 \\\\ \implies r^3 - 27 = 0 \\\\ \implies r^3 = 27 \implies \boxed{r=3}

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Gus has a lunch food budget of $190 per month. He spends an average of $5 per day on lunch. Which of the following equations rep
olganol [36]

Answer:

The answer is C.

Step-by-step explanation:

Each day (x) he loses 5 dollars from his total of 190. And C shows that because 190 - 5 x. 190 is his total, 5 is dollars lost a day, and x is days

3 0
3 years ago
How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? a.119 b.16,
Sergeeva-Olga [200]
Answer:
c. 2520

Explanation:
Repetition is not allowed, therefore:
1st digit can be any of the given 7 numbers
2nd digit can be any of the remaining 6 numbers
3rd digit can be any of the remaining 5 numbers
4th digit can be any of the remaining 4 numbers
5th digit can be any of the remaining 3 numbers
This means that:
number of possible combinations = 7 * 6 * 5 * 4 * 3 = 2520 numbers

Hope this helps :)
5 0
3 years ago
Solve the inequality for <br> 8w-35&lt; 3−(5-4w)<br><br> Simplify the answer as much as possible
Finger [1]

Answer:

w<33/4

Step-by-step explanation:

8w-35<3-(5-4w)

8w-35<3-5+4w

8w-35<-2+4w

8w-4w-35<-2

4w-35<-2

4w<-2+35

4w<33

w<33/4

7 0
3 years ago
10 x 4 ones = how many ones
Alisiya [41]
The product will be 40 I believe?
3 0
3 years ago
What is the value of x?<br><br> 27(x+4)=−6<br><br><br> −35<br><br> −25<br><br> 25<br><br> 35
Oksanka [162]

x = -38/9 !!!


27(x+4)=−6

Step 1: Simplify both sides of the equation.

27(x+4)=−6

(27)(x)+(27)(4)=−6 (Distribute)

27x+108=−6

Step 2: Subtract 108 from both sides.

27x+108−108=−6−108

27x=−114

Step 3: Divide both sides by 27.

27x/27=−114/27

x=−389

6 0
3 years ago
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