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3 years ago

Find the sum of the first seven terms of the sequence 4, 12, 36, 108, … .

Mathematics

1 answer:

bulgar [2K]3 years ago

3 0

The given sequence is 4,12,36,108....

Here we can observe the first term $a_{1}$ = 4 , $a_{2}=12$ and so on.

The common ratio (r)= $\frac{12}{4}=3$

Since the common ratio is greater than 1,

Therefore the sum of the geometric series = $\frac{a(r^{n}-1)}{r-1}$

Since we have to find the sum of first seven terms, so n=7

= $\frac{4(3^{7}-1)}{3-1}$

=4372.

Therefore, option C is the correct answer.

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Each week, a cook purchases 12 pounds of butter. During the last year, the cook has paid as little as $23.04 and at much as $29.

Tatiana [17]

Each week, a cook purchased 12 LBS. of Butter:

During the Last year: (12 Months):

Cook Paid:

Little: $23.04

Much: $29.40, For Butter he or she purchased in a week:

Question: is: what is the Difference between, the Greatest price per pound, and the least price per pound of butter the cook paid within the last year?

EQUATION:

Least Paid / 12 =====> 23.04 /12

Most Paid / 12 ======> 29.40 / 12

Divide:

23.04 / 12 = 1.92 / LB

29.40 / 12 = 2.45 / LB

Now Subtract:

2.45 - 1.92

Answer ======> 0.53 is the difference, between the greatest price per round, and least price per round of butter the cook would have paid within the last year.

Hope that helps!!! : )

4 0

3 years ago

find the formula for a rational function that satisfies all of the following. its x-intercept is (-3,0). it has a vertical asymp

Norma-Jean [14]

Let that be

$\\ \rm\Rightarrow y=\dfrac{a(f(x))}{g(x)}$

Two vertical asymptotes at -1 and 0

$\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x(x+1)}$

If we simply

$\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x^2+1}$

Denominator has degree 2
Numerator should have degree as 2 and coefficient as 3 inorder to get horizontal asymptote y=3 means the quadratic equation should contain 3x²
But there should be a x intercept at -3 so one zeros should be -3

Find a equation

3x²+9x

Find zeros

3x²+9x=0
3x(x+3)=0
x=0,-3

Horizontal asymptote

3x²/x²
3

So our equation is

$\\ \rm\Rightarrow y=\dfrac{3x^2+9x}{x(x+1)}$

Graph attached

4 0

2 years ago

A total of 75 cookies and cakes were donated for a bake sale to raise money for the football team. There were four times as many

MArishka [77]

Answer:

Step-by-step explanation:

15*4 = 60

15+60= 75

6 0

3 years ago

Read 2 more answers

Suppose that the second term of a geometric sequence is 4 and the sixth term is 16. Find the fourth term

Kaylis [27]

Answer:

Step-by-step explanation:

<h3>Given GP</h3>

a₂ = 4,
a₆ = 16

a₄ = ?

<h3>Solution</h3>

a₂ = ar = 4
a₆= ar⁵ = 16

<u>Substitute ar in the second equation</u>

ar⁵= 16
4r⁴ = 16
r⁴ = 4
r = √2

<u>Then finding a₄</u>

a₄ = a₂*r² = 4*(√2)² = 4*2= 8

7 0

3 years ago

Can someone please help me with this!

Virty [35]

The answer for number 3 is 3.c

5 0

3 years ago

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