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4 years ago

What is the value of the 9th term in the following geometric sequence?

Mathematics

1 answer:

earnstyle [38]4 years ago

7 0

Answer: The correct option is (D) 196608.

Step-by-step explanation: We are given to find the value of the 9th term in the following geometric sequence :

3, 12, 48, 192, . . .

We know that

the n-th term of a geometric sequence with first term a and common ratio r is given by

$a_n=ar^{n-1}.$

For the given sequence, we have

first term, a = 3 and the common ratio, r is given by

$r=\dfrac{12}{3}=\dfrac{48}{12}=\dfrac{192}{48}=~~.~~.~~.~~=4.$

Therefore, the 9th term of the given sequence will be

$a_9=ar^{9-1}=3\times 4^8=3\times65536=196608.$

Thus, the required 9th term of the given sequence is 196608.

Option (D) is CORRECT.

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Rachel has taken 6 tests so far and has received scores of 83%, 92%, 79%, 88%, 89%, and 95%. What must Rachel receive on her sev

Vinil7 [7]

Let the score on her seventh test be "x".

SO,

$\frac{83+92+79+88+89+95+x}{7} =90\\\\ \frac{526+x}{7}=90\\\\ 526+x=630\\\\x=630-526\\\\ \boxed{x=104}$

∴ He must get 104% on his seventh test to get an average score of 90%

5 0

3 years ago

Read 2 more answers

Is f(x) continuous at x equals 4? Why or why not? A. No, f(x) is not continuous at x equals 4 because ModifyingBelow lim Wit

soldier1979 [14.2K]

<u>Corrected Question</u>

Is the function given by:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

continuous at x=4? Why or why not? Choose the correct answer below.

Answer:

(D) Yes, f(x) is continuous at x = 4 because $Lim_{x \to 4}f(x)=f(4)$

Step-by-step explanation:

Given the function:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

A function to be continuous at some value c in its domain if the following condition holds:

f(c) exists and is defined.

$Lim_{x \to c}$ f(x)$ exists.

$f(c)=Lim_{x \to c}$ f(x)$

At x=4

$f(4)=\dfrac{1}{4}*4+1=2$

$Lim_{x \to 4}f(x)=2$

Therefore: $Lim_{x \to 4}f(x)=f(4)=2$

By the above, the function satisfies the condition for continuity.

The correct option is D.

3 0

3 years ago

1. Add or subtract. Show your work for each problem.

Aleks04 [339]

Hi there!

a. 8x^2 - 1
(x^2 - 4x + 5) + (7x^2 + 4x - 6)
= x^2 + 7x^2 - 4x + 4x - 1
= 8x^2 - 1

b. 5x^2 + 7x - 7
(7x^2 + 4x - 6) - (2x^2 - 3x + 1)
= 7x^2 + 4x - 6 - 2x^2 + 3x - 1
= 7x^2 - 2x^2 + 4x + 3x - 6 - 1
= 5x^2 + 7x -7

Hope this helps!

4 0

4 years ago

Binomial theorem Expand (5 - y)3

Snowcat [4.5K]

Answer:

(5 - y) ^3 = 125 - 75y + 15y^2 - y^3

Step-by-step explanation:

Binomial expression

1. 1

1. 2. 1

1. 3. 3. 1 --------power of 3

( 5 - y) ^3

( 5 - y) (5 - y) (5 - y)

( a + b) ^3 = a^3 + 3a^2b + 3ab^2 + b^3

a = 5

b = -y

( 5 - y) ^2 = ( 5 - y) (5 - y)

= 5( 5 - y) - y(5 - y)

= 25 - 5y - 5y + y^2

=(25-10y+y^2)

( 25 - 10y + y^2)( 5 - y)

= 5(25 - 10y + y^2) - y( 25 - 10y + y^2)

= 125 - 50y + 5y^2 - 25y + 10y^2 - y^3

Collect the like terms

= 125 - 50y - 25y + 5y^2 + 10y^2 - y^3

= 125 - 75y + 15y^2 - y^3

7 0

3 years ago

Passes through (3,5) and (-1,5)

AlladinOne [14]

Presumably we're being asked for the line which passes through (3,5) and (-1,5) which is simply $y=5.$

3 0

3 years ago