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katen-ka-za [31]

3 years ago

7

#5 Points possible: 3. Total attempts: 5

1 answer:

kirill115 [55]3 years ago

4 0

Answer:

honesty you cant realy use a calculator because you need to meadian mode and range them first

Step-by-step explanation:

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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

3 years ago

Pass a brotha some help :(

nikitadnepr [17]

Answer and Step-by-step explanation:

Distribute the 1p to the y and -6 and distribute the 2 to the 3y and 6.

10y - 50 + 6y + 12

Now, combine like terms.

16y - 38

#teamtrees #PAW (Plant and Water)

7 0

3 years ago

You buy 11 bagels with a 20$ bill how m if change do you receive? how many bagels could you buy?

Svetllana [295]

Change you’ll receive is = 0.09
you can only buy 11 because if you divide 20/11 it will give you 1.81 and if you multiply 11x 1.81 it will give you 19.91 which is close to $20 & that’s the most you can buy .

5 0

3 years ago

3 girls share $680 in the ratio 9 : 7 : 4, show that adele receives $306

Korolek [52]

Answer:

=$306

Step-by-step explanation:

9/20*$680

4 0

3 years ago

Can a triangle be formed with the given lengths 9 in, 12 in, 18 in?

balandron [24]

9+12>18
12+18>9
9+18>12

So, yes. A triangle can be formed by the given angles.

4 0

3 years ago

Read 2 more answers