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3 years ago

Write the explicit formula for the sequence below and use it to find the 16th term:

Mathematics

1 answer:

mario62 [17]3 years ago

3 0

Given:

The sequence is:

$6, -24, 96, -384,...$

To find:

The explicit formula for the given sequence and then find the 16th term.

Solution:

We have,

$6, -24, 96, -384,...$

The ratio between two consecutive terms are:

$\dfrac{-24}{6}=-4$

$\dfrac{96}{-24}=-4$

$\dfrac{-384}{96}=-4$

The given sequence has a common ratio. So, the given sequence is a geometric sequence with first term 6 and common ratio $-4$ .

The explicit formula of a geometric sequence is:

$a_n=ar^{n-1}$

Where, a is the first term and r is the common ratio.

Putting $a=6, r=-4$ in the above formula, we get

$a_n=6(-4)^{n-1}$

We need to find the 16th term. So, put $n=16$ in the above formula.

$a_n=6(-4)^{16-1}$

$a_n=6(-4)^{15}$

$a_n=6(-1073741824)$

$a_n=-6442450944$

Therefore, the explicit formula for the given sequence is $a_n=6(-4)^{n-1}$ and 16th term of the given sequence is $-6.442450944$ .

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sveticcg [70]

<h2>>>> Answer <<<</h2>

Let's check which polynomial is divisible by ( x - 1 ) using hit , trial and error method .

A ( x ) = 3x³ + 2x² - x

The word " divisible " itself says that " it is a factor "

Using factor theorem ;

Let;

=> x - 1 = 0

=> x = 1

Substitute the value of x in p ( x )

p ( 1 ) =

3 ( 1 )³ + 2 ( 1 )² - 1

3 ( 1 ) + 2 ( 1 ) - 1

3 + 2 - 1

5 - 1

This implies ;

A ( x ) is not divisible by ( x - 1 )

Similarly,

B ( x ) = 5x³ - 4x² - x

B ( 1 ) =

5 ( 1 )³ - 4 ( 1 )² - 1

5 ( 1 ) - 4 ( 1 ) - 1

5 - 4 - 1

5 - 5

This implies ;

B ( x ) is divisible by ( x - 1 )

Similarly,

C ( x ) = 2x³ - 3x² + 2x - 1

C ( 1 ) =

2 ( 1 )³ - 3 ( 1 )² + 2 ( 1 ) - 1

2 ( 1 ) - 3 ( 1 ) + 2 - 1

2 - 3 + 2 - 1

4 - 4

This implies ;

C ( x ) is divisible by ( x - 1 )

Similarly,

D ( x ) = x³ + 2x² + 3x + 2

D ( 1 ) =

( 1 )³ + 2 ( 1 )² + 3 ( 1 ) + 2

1 + 2 + 3 + 2

This implies ;

D ( x ) is not divisible by ( x - 1 )

<h2>Therefore ; </h2>

<h3>B ( x ) & C ( x ) are divisible by ( x - 1 ) </h3>

6 0

3 years ago

Whats992,449 rounded to the nearest hundred thousand

Andreas93 [3]

Yep, the answer is 1,000,000. To explain the process of how the answer is figured out, the 9 next to the 9 in the hundred thousand's place tells us that we need to round up. So, we'd be rounding up to 1,000,000. Hope this helped you understand it :)

3 0

3 years ago

Read 2 more answers

On a spinner, there are twenty equal-size sections numbered from 1 to 20. Which spinner game is fair? Show your work.

Anvisha [2.4K]

The spinner game is an illustration of probability, and the spinner game that is fair is (b) If you spin a number greater than 10, you win.

<h3>How to determine the fair game?</h3>

The number of sections in the spinner is given as:

n = 20

There are 10 numbers greater than 10 i.e. 11 to 2.

So, the probability that a number greater than 10 is spun is:

P = 10/20

P = 0.5

The probability that a number that is not greater than 10 is spun is calculated using the following complement rule

q = 1 - p

This gives

q = 1 - 0.5

Evaluate

q = 0.5

Notice that both probabilities are the equal

Hence, the spinner game that is fair is (b) If you spin a number greater than 10, you win.