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r-ruslan [8.4K]

2 years ago

5

Which of these statements is true?

1 answer:

Snezhnost [94]2 years ago

7 0

Answer:

C

Step-by-step explanation:

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Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...

katovenus [111]

Answer:

$a_{12}=-244140625$

Step-by-step explanation:

Considering the geometric sequence

$5,-25,\:125,\:...$

$a_1=5$

As the common ratio ' $r$ ' between consecutive terms is constant.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$r=\frac{-25}{5}=-5$

$r=\frac{125}{-25}=-5$

The general term of a geometric sequence is given by the formula:

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

where $a_1$ is the initial term and $r$ the common ratio.

Putting $n = 12$ , $r = -5$ and $a_1=5$ in the general term of a geometric sequence to determine the 12th term of the sequence.

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

$a_n=5\left(-5\right)^{n-1}$

$a_{12}=5\left(-5\right)^{12-1}$

$=5\left(-5^{11}\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=-5\cdot \:5^{11}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

$=-5^{1+11}$ ∵ $5\cdot \:5^{11}=\:5^{1+11}$

$=-244140625$

Therefore,

$a_{12}=-244140625$

6 0

2 years ago

Can someone Help me in this problem?

Fed [463]

If you have to write the equation then it would be "5k + 6.7"

5 0

2 years ago

Pls help!!!! <br>Evaluate the permutations <br><br><br>1. 6P2<br><br>2. 7P4<br><br>3. 8P3<br><br>

Gnom [1K]

Answer:

5p9

Step-by-step explanation:

4 0

3 years ago

If mce =40 and m cde =30 what is mab

deff fn [24]

The measure of arc AB is 100°.

3 0

2 years ago

Solve for x and explain how you got your answer <br> 3x + 4 = 16

12345 [234]

Answer:

X = 4

Step-by-step explanation:

3x=16-4

3x= 12

X=12/3

X= 4

5 0

3 years ago