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Oksi-84 [34.3K]
2 years ago
15

Enter a recursive rule for the geometric sequence. 6, −18, 54, −162, ...

Mathematics
1 answer:
svlad2 [7]2 years ago
5 0

Answer:

The required recursive formula is:

a_n=(-3)\times a_{n-1}

Step-by-step explanation:

We are given a geometric sequence as:

6,-18,54,-162,.....

Clearly after looking at different terms of the sequence we could observe that the sequence is an geometric progression (G.P.) with common ratio= -3 denoted by r.

Let a_n represents the nth term of the sequence.

This means that:

a_1=6, a_2=-18, a_3=54, a_4=-162,......

As the common ratio is -3.

so,

a_1=6\\\\a_2=-18=(-3)\times a_1\\\\a_3=54=(-3)\times a_2\\\\.\\.\\.\\.\\.\\.\\.\\.\\.a_n=(-3)\times a_{n-1}

Hence, the required recursive formula for the geometric sequence is:

a_n=(-3)\times a_{n-1}

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Ashley plants a tree 45cm tall it grows by 10 cm each year. Find the amount ashley gets in the 5th year?​
Genrish500 [490]

Answer:

95cm

Step-by-step explanation:

45cm is the initial height

each year grow 10cm

growing time 5 years

45+(10 × 5)=95 cm

4 0
2 years ago
Reyna has 5 coins worth 10 cents each and 4 coins
Zolol [24]

Answer:

The Probability found is:

P =  \frac{13}{18}

Step-by-step explanation:

Let x be the 10 cents coin.

Let y be the 25 cents coin.

We have to find all the possible outcomes

1) First coin = 10 cents, Second coin = 10 cents , so

(x,x) = 20

2) First coin = 10 cents, Second coin = 25 cents , so

(x,y) = 35

3) First coin = 25 cents, Second coin = 10 cents , so

(y,x) = 35

4) First coin = 25 cents, Second coin = 25 cents , so

(y,y) = 50

Find the probability of each outcome:

P(x,x) =  \frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}

P(x,y) =  \frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}

P(y,x) =  \frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}

P(y,y) = \frac{4}{9}\cdot\frac{3}{8}=\frac{12}{72}

Add all the probabilities where sum is at least 35 i.e P(x,y) , P(y,x) , P(y,y)

P(x,y) + P(y,x) + P(y,y) = \frac{20}{72}+\frac{20}{72}+\frac{12}{72} = \frac{52}{72}=\frac{13}{18}\\

6 0
2 years ago
Todd's friend Olivia is flying her stunt plane at an elevation of 6.3 km. From the ground, Todd's used to plane moving directly
Aloiza [94]
Can't understand the sentence where it says "<span>From the ground, Todd's used to plane moving directly toward him from the West at a 49 degree angle of elevation". Help me interpret it.</span>
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Evaluate 4 - 0.25g + 0.5h when g = 10 and h = 5
Jlenok [28]

Answer:

4

Step-by-step explanation:

Well first we need to plug in 10 for g and h for 5.

4 - .25(10) + .5(5)

4 - 2.5. + 2.5

1.5 + 2.5

= 4

<em>Thus,</em>

<em>the answer is 4</em>

<em />

<em>Hope this helps :)</em>

3 0
2 years ago
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Find the quotient. (5x4 – 3x2 4) ÷ (x 1)
Vlada [557]

Keywords:

<em>Divide, polynomial, quotient, divisor, dividend, rest </em>

For this case, we must find the quotient by dividing the polynomial (5x ^ 4-3x ^ 2 + 4)\ by\ (x + 1). We must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the rest, as shown in the attached figure. At the end of the division, to verify we must bear in mind that:

Dividend = Quotient * Divider + Remainder

Answer:

See attached image

4 0
2 years ago
Read 2 more answers
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