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slamgirl [31]
2 years ago
12

Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. -2, 6, -18, 54,

...
Mathematics
1 answer:
aleksandrvk [35]2 years ago
3 0

Answer:

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio,r. Considering the given sequence,

r = 6/- 2 = - 18/6 = - 3

Therefore, the sequence is geometric.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = - 2

r = - 3

The explicit formula is

Tn = - 2 × (- 3)^(n - 1)

To find the 8th term, T8,

T8 = - 2 × (- 3)^(8 - 1)

T8 = - 2 × (- 3)^7

T8 = - 2 × - 2187

T8 = 4374

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a tourist drove his car for the total of 17.5 hours while on a 3-day vacation on the first day he drove 4.5 hours in the second
AleksAgata [21]

Answer:

1.75 hours

Step-by-step explanation:

Time for day 1 : 4.5 hrs

Time for day 2: (4.5 ×2.5)

Time for day 3: let it be denoted by a variable ,say T.

Total Time= 17.5

(Time for day 1 ) + (Time for day 2) +(Time for day 3) =17.5

4.5 + (4.5×2.5) + T = 17.5

4.5+11.25+T =17.5

15.75+T=17.5

T=17.5-15.75

T= 1.75

7 0
3 years ago
For a sequence defined by f(1)=13 and 2f(n-1)+(n-2), which of the following is the value of f(4)
densk [106]
Given that:
f(1)=13 and 2f(n-1)+(n-2)
then:
f(4) will be found as follows:
f(2)=2f(2-1)=2f(1)=2*13=26
f(3)=2f(3-1)+(3-2)=2f(2)+1=2*26+1=53
f(4)=2f(4-1)+(4-2)=2f(3)+(4-2)=2(53)+2=108

Thus:
Answer:(3) 108

6 0
2 years ago
Which of the following inequalities have -8 in its solution set?
BaLLatris [955]

Answer:

3x >/= 24 or 3x </= -24

Step-by-step explanation:

Plug in (-8) for (x) and solve.

8 0
3 years ago
Please help me someone
Jobisdone [24]

Answer: itz d plz trust me

4 0
2 years ago
Sandra uses her office fax machine to send fax at the rate of $0.10 per page. She decides to rent a fax machine for $80 a year.
Maksim231197 [3]
Part A: 
 First we define the variable to be used for the problem:
 x: the number of pages that Sandra should fax
 The inequality for rent is:
 0.06x <= 80
 Note that the price will be less than using the fax from the office, since for the same number of pages, we have:
 y = 0.10x
 Answer:
 
an inequality that can be used to calculate the number of pages that Sandra should fax in a year is:
 
0.06x <= 80

 Part B:
 0.06x <= 80
 From here we clear x:
 x <= 80 / 0.06
 x <= 1333.33333
 Nearest whole number
 x <= 1333
 Sandra can use the leased fax for 1333 pages and the cost will be:
 1333 * 0.06 = 79.98 $
 Using the office fax the cost will be:
 1333 * 0.1 = 133.3 $
  Answer:
 
By renting the sara machine, you save:
 
133.3-79.98 = 53.32 $
8 0
3 years ago
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