Mathematics, 29.12.2020 08:00, KariSupreme

3. The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising. (a) What is the recursive rule for the sequence? (b) What is the iterative rule for the sequence?

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answered: bartonamber4042

a) The recursive rule for the sequence is $a_n=3a_{n-1}$

b) The iterative rule for the sequence is a_n=2(3^n)

The given sequence is:

6, 18, 54, 162, …

The common ratio, r = 18/6

r = 3

Let the last term be a_n

Let the preceding term be $a_{n-1}$

The recursive rule for the sequence is given as:

$a_n=a_{n-1}r\\\\a_n=3a_{n-1}$

b) The iterative rule is gotten by using the formula:

$a_n=ar^{n-1}$

Substitute a = 6 and r = 3 into the formula above

$a_n=6(3)^{n-1}\\\\a_n=\frac{6}{3}(3^n )\\\\a_n=2(3^n)$

Learn more on sequence here: link

answered: babyissy2016

Please check the explanation.

Step-by-step explanation:

(a) What is the recursive rule for the sequence?

Given the sequence

6, 18, 54, 162,...

Please note that each successive term is 3 times the previous term.

i.e. 18 = 6×3, 54 = 18×3, 162 = 54×3

Here, r = 3 is the common multiplier

In other words, every next term can be obtained by multiplying the previous term by a number 'r', using the recursive formula

$a_n=a_{n-1}\times r$

Here, aₙ is r times the previous term aₙ₋1.

For example, in order to determine the 2nd term a₂, just put n=2 in the recursive formula

$a_n=a_{n-1}\times r$

so substituting r = 3, and n = 1 in the recursive formula

$a_2=a_{2-1}\times 3$

$a_2=a_1\times \:3\:\:\:\:\:\:$

a₁ = 6

$a_2=6\times \:3\:\:\:\:\:\:$

a_2=18

(b) What is the iterative rule for the sequence?

Given the sequence

6, 18, 54, 162,...

A geometric sequence has a constant ratio 'r' and is defined as

$a_n=a_1\cdot r^{n-1}$

$\frac{18}{6}=3,\:\quad \frac{54}{18}=3,\:\quad \frac{162}{54}=3$

The ratio of all the adjacent terms is the same and equal to, so

r = 3

a₁ = 6

so substituting r = 3 and a₁ = 6 in the nth term of the sequence

$a_n=a_1\cdot r^{n-1}$

$a_n=6\cdot \:3^{n-1}$

Thus, the iterative rule for the sequence is

$a_n=6\cdot \:3^{n-1}$

answered: Guest

2.56 is the width of the garden

step-by-step explanation:

answered: Guest

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: