All categories

1 year ago

Find the sum of the first five terms using the geometric series formula for the sequence 1/2, -1,2,-4…

Mathematics

1 answer:

sammy [17]1 year ago

7 0

The sum of the first five terms is 11/2

<h3>How to determine the sum?</h3>

The series is given as:

1/2, -1,2,-4…

Calculate the common ratio of the series using

r = -4/2

Evaluate

r = -2

The sum is then calculated as:

$S_n = a\frac{1 - r^n}{1 - r}$

This gives

$S_n = \frac{1}{2} * \frac{(1 - (-2)^5}{1 + 2}$

Evaluate

$S_n = \frac{1}{2} * \frac{33)}{3}$

Evaluate

$S_n =\frac{11}{2}$

Hence, the sum of the first five terms is 11/2

You might be interested in

If 5/12 visitors are adults and 3/10 were men what fraction were men?

Zigmanuir [339]

You need to do the following equation:

(5/12)*(3/10)

5*3=15

12*10=120

15/120=5/40 of the adults who visited were men.

6 0

3 years ago

Read the paragraph. Replace each underlined noun by writing a pronoun above it.

rewona [7]

Answer:

Step-by-step explanation:

She

Her

Their

They

Their

They

Him

7 0

3 years ago

It takes 45 minutes to drive to the nearest bowling alley taking city streets going 30 miles per hour

zmey [24]

Answer:

The time it will take to get to the bowling alley while driving at 65 mph on the freeway is approximately 20.8 minutes

Step-by-step explanation:

The given parameters are;

The time it takes through the streets to drive to the nearest bowling alley = 45 minutes

The speed of driving through the streets = 30 miles per hour (mph)

The speed of driving through the freeway to the bowling alley = 65 mph

From the speed of driving through the streets and the time taken we have;

The formula for speed, S, is S = Distance/Time

Therefore, 30 mph = Distance/45 minutes

Where, 1 hour = 60 minutes, 45 minutes = 1/60×45 hour = 3/4 hour

30 mph = Distance/45 minutes = Distance/(3/4 hour)

30 mph = Distance/(3/4 hour)

Distance = 30 mph × 3/4 hour = 22.5 miles

Given that the distance through the freeway and through the streets are the same, we have from speed = Distance/Time;

Time = Distance/Speed

The speed through the freeway = 65 mph while the distance remain 22.5 miles

Therefore;

Time = 22.5 miles/(65 mph) ≈ 0.346 hour ≈ 20.8 minutes

The time it will take to get to the bowling alley while driving at 65 mph on the freeway is approximately 20.8 minutes.

8 0

3 years ago

Find the slope of the line passing through (-7,-8) and (5,-8)

zhenek [66]

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, - 8) and (x₂, y₂ ) = (5, - 8)

m = $\frac{-8+8}{5+7}$ = $\frac{0}{12}$ = 0

8 0

3 years ago

Describe the translation represented by the rule (x, y) → (x + 3, y – 2)?

Veronika [31]

The translation, <span> (x, y) → (x + 3, y – 2), means that the point on the X-axis would move 3, and because it's positive, it would move to the right 3.
Y</span>– 2 means the point on the Y-axis moves 2, and because it is negative 2 it moves down 2

3 0

3 years ago

Read 2 more answers