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3 years ago

5

Which of the following expressions has a value of 5? Select all that apply.

1 answer:

worty [1.4K]3 years ago

6 0

Answer: all that has value of 5

A. -3 - (-8)

B. -1 + 6

D. 2 - (-3)

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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

1, 1, 5, 5, 7, 8, 8, 10, 12

stepan [7]

Answer:

ррооо

Step-by-step explanation:

Нажмите на фрагмент, чтобы вставить его в текстовое поле.

4 0

1 year ago

Help please geometry !

Leona [35]

If you use the same technique from the first question, you can do:

5x+2=3x+42
2x=40
x=20

For the rest of the questions, please use the same technique if they are vertical because I can't solve all of the questions for you sorry.

4 0

2 years ago

100 is the sum of 25 and Num

Slav-nsk [51]

Algebraic expression: 100 = 25 + n

Answer: n = 75

7 0

2 years ago

Solve the system of inequalities by graphing. y< – 5 y≤ – 6x–3

Lorico [155]

Answer: Not too sure. Sorry.

Step-by-step explanation:

6 0

2 years ago