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3 years ago

What is the common difference for the sequence shown below?

Mathematics

2 answers:

Alex Ar [27]3 years ago

4 0

It is B because for every point going down, there is 3 to the left and so it is 1/3 and it has to be negative because its going left

jeka57 [31]3 years ago

3 0

Answer:

Option 2nd is correct

$-\frac{1}{3}$

Step-by-step explanation:

The nth term for the arithmetic sequence is given by:

$a_n = a+(n-1)d$

where,

$a_1$ is the first term

d is the common difference

n is the number of terms.

As per the statement:

From the given graph:

At n =1

$a_1 =4$

At n =4

$a_4=3$

Using the nth term formula for the arithmetic sequence:

$a_4 = a_1+3d$

Substitute the given values we have;

$3 = 4+3d$

Subtract 4 from both sides we have;

$-1 = 3d$

Divide both sides by 3 we have;

$-\frac{1}{3} =d$

$d =-\frac{1}{3}$

Therefore, the common difference for the given sequence as shown is, $-\frac{1}{3}$

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Evaluate y = ex + 1 for the following values of x. Round to the nearest thousandth. x = −2, y ≈ x = 1, y ≈ x = 2, y ≈

soldier1979 [14.2K]

The equation is not clear whether it is $y= e^{x+1}$ or $y= e^{x} +1$

for $y= e^{x+1}$

$x=-2$ ⇒ $e^{-2+1}=0.37$
$x=1$ ⇒ $e^{-1+1} = e^{0}=1$
$e^{2+1}= e^{3}=20.10$

for $y= e^{x}+1$

$x=-2$ ⇒ $y=e^{-2}+1 =1.14$
$x=1$ ⇒ $y= e^{1} +1=3.72$
$x=2$ ⇒ $y= e^{2}+1=8.39$

Hint: Most scientific calculators have the template of $e^{( )}$ which you can use to work out the value of y