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2 years ago

What is the sum of the geometric sequence-1,6,36 if there are 6 terms

Mathematics

1 answer:

Reptile [31]2 years ago

5 0

Answer:

The sum is $9,331$

Step-by-step explanation:

we have

$1,6,36,...$

we have

$a1=1$

$a2=6$

$a3=36$

Find the common ratio r

$a2/a1=6/1=6$

$a3/a2=36/6=6$

The common ratio is r=6

The formula to calculate the sum in a geometric sequence is equal to

$S=a1\frac{(1-r^{n})}{(1-r)}$

where

n is the number of terms

r is the common ratio

a1 is the first term

we have

$n=6$

$a1=1$

$r=6$

substitute

$S=(1)\frac{(1-(6)^{6})}{(1-6)}$

$S=\frac{(1-(6)^{6})}{(-5)}$

$S=9,331$

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In Leakwater township, there are two plumbers. On a particular day three Leakwater residents call village plumbers independently

Marianna [84]

Answer:

25% probability that all three residents will choose the same plumbe

Step-by-step explanation:

For each resident, there are only two possible outcomes. Either they choose the first plumbe, or they choose the second. The plumbers are chosen independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each resident randomly chooses one of the two plumbers.

This means that $p = \frac{1}{2} = 0.5$

Three residents:

This means that $n = 3$

What is the probability that all three residents will choose the same plumb

This is P(X = 0)(all choose the second pumble) or P(X = 3)(all choose the first pumble). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.5)^{0}.(0.5)^{3} = 0.125$

$P(X = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125$

$p = P(X = 0) + P(X = 3) = 2*0.125 = 0.25$

25% probability that all three residents will choose the same plumbe

4 0

2 years ago

What is the slope of the line

ki77a [65]

Answer:

gradient =rise/run

Rise/run=4/4

4/4=1

Have a nice Day , Hope this helped you I would appreciate it if you could mark my answer brainliest

4 0

2 years ago

Find the first four nonzero terms in a power series expansion about xequals0 for the solution to the given initial value problem

IgorC [24]

Answer:

The first four terms are;

w(x)= 4 + 2x² - ⁵/₆x⁴+ ¹¹/₃₆x⁶ +......

Step-by-step Explanation:

This is the interpretation of the question

w″ + 3xw′ -w=0

W(0)=4

W′(0)=0

CHECK THE ATTACHMENT FOR STEP BY STEP EXPLANATION

7 0

3 years ago

A scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the

almond37 [142]

Answer:

s = 4

Step-by-step explanation:

The equation for the line of best fit for the data is p=25s+40.

Where p is no. of points and s is no. fo strikes

We need to find the number of strikes made by a bowler with 140 points.

Put p = 140

p=25s+40

140 = 25s+40

Subtract 40 to both sides,

140-40 = 25s+40-40

100 = 25s

⇒ s = 4

So, there are 4 strikes made by a bowler with 140 points.

5 0

2 years ago

Scott earned 20 points more on his most recent math test than he earned on the previous test. If he earned at least 80 points on

NARA [144]

9514 1404 393

Answer:

s ≥ 60

Step-by-step explanation:

If Scott earned 20 points more on this test, then he earned 20 points less on the last test. 20 points less than "at least 80" is "at least 60."

s ≥ 60

7 0

2 years ago