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2 years ago

6

If you know the seventh term in an arithmetic sequence and the common difference,

1 answer:

Pachacha [2.7K]2 years ago

3 0

Yes-because from the 7th term you can either go backwards or forwards to find the number/pattern/letter you need to get to

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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$

8 0

2 years ago

Given g(x)=2x-1, solve for x when g(x)=3.

SashulF [63]

Answer:g(x)=2(3)+1=6+1=7

Step-by-step explanation:7

7 0

2 years ago

Read 2 more answers

A line includes the points (4, 8) and (3, 5). What is its equation in slope-intercept form? Write your answer using integers, pr

stich3 [128]

Answer:

A line includes the points (4, 8) and (3, 5) whose equation in slope-intercept form will be :

$y=3x-4$

Step-by-step explanation:

The point slope form: $(x_1,y_1) and(x_2,y_2)$

$(y-y_1)=m(x-x_1)$

where : m = Slope of the line

$m=\frac{y_2-y_1}{x_2-x_1}$

A line includes the points (4, 8) and (3, 5).The equation of the line will be:

$m=\frac{5-8}{3-4}=3$

$(y-8)=3\times (x-4)$

$y-8=3x-12$

$y=3x-4$

(y=mx+c), where c is intercept at y axis.

The above equation represents slope-intercept form of the line.

6 0

2 years ago

Jason paid $50 to be a member of the Anglin Mighty Gym. When he takes 2 points

polet [3.4K]

Answer:

It will never cost the same amount.

But, It would take 5 classes for Erik to pass Jason.

Step-by-step explanation:

Jason: 5 classes×$2 per class=$10+$50=60$

Erik: $13×5 classes= $65

5 0

2 years ago

Suppose the odds against winning the lottery as 48,000,000 to 1. What is the probability of the event of winning the lottery giv

kupik [55]

The probability according to the given scenario will be " $\frac{1}{48,000,001}$ ".

According to the question:

The odds against winning the lottery are 48,000,000 to 1.
Favorable outcome = 1

→ The total outcome will be:

= $48,000,000 +1$

= $48,000,001$

As we know,

→ $P(E) = \frac{Favorable \ outcomes}{Total \ outcomes}$

By putting the values, we get

→ $=\frac{1}{48,000,001}$

Thus the above response is right.

Learn more about Probability here:

brainly.com/question/15739211

8 0

1 year ago