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3 years ago

Can someone please help me with this math question?

Mathematics

1 answer:

mash [69]3 years ago

8 0

3b+3s will be the answer

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The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

2 years ago

X^3+6x^2-17x+2-x^3-x^2-11x+36

Rudiy27

<span>X^3+6x^2-17x+2-x^3-x^2-11x+36 = </span>5x^2 - 28x + 38

4 0

2 years ago

8.) 2x<12 pls help me

Roman55 [17]

Answer:

x < 6

Step-by-step explanation:

2x < 12

Divide both sides by 2;

x < 6

x is less than 6

3 0

2 years ago

What is 0.16666666...as fraction .show your work

Alecsey [184]

<h3>Answer: 1/6</h3>

Work Shown:

x = 0.1666666...

10x = 1.666666...

100x = 16.666666...

100x - 10x = 16.666666... - 1.666666...

90x = 15

x = 15/90

x = (1*15)/(6*15)

x = 1/6

So, 1/6 = 0.1666666...

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2 years ago

Round 37,218 to the nearest ten thousand. Show your work

tensa zangetsu [6.8K]

The answer is 36,000 because it is not over 36,500

6 0

2 years ago