All categories

3 years ago

Calculate the 5th term of the sequence which has this explicit formula: an=3/2n(2n+5), n=1,2,...

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

8 0

Answer:

D. 9 ÷ 2

Step-by-step explanation:

For getting the nth value of the sequence we simply put the value of n in a formula.

In the given sequence for finding the 5th term we simply put n = 5 in given explicit formula:

We have $a_{n} = \frac{3}{2n}(2n+5)$

Putting n = 5

$a_{5} = \frac{3}{2\times5}(2\times5+5)$

⇒ $a_{5} = \frac{3}{10}(15)$

⇒ $a_{5} = \frac{9}{2}$

Thus, option (D) is correct.

You might be interested in

You are remodeling your kitchen. You've contacted two tiling companies who gladly told you how long it took their workers to til

quester [9]

Ok so pete lays 10 more than jim per hour

pete and jim laid same amount of tiles

j=jim's rate
p=pete's rate

6j=5p

but pete lays 10 tile per hour faster so
p=10+j

sub
6j=5(10+j)
6j=50+5j
minus 5j both sides
j=50

jim can lay at 50 tiles per hour

7 0

3 years ago

Read 2 more answers

Find a slope of the line that passes through (7,-4) and (81,92)

Leokris [45]

Answer:

48/37

Step-by-step explanation:

Use the formula (y1 - y2)/(x1 - x2).

Plug in your x and y values to get (92 + 4)/(81 - 7).

Simplify down to get 96/74 and simplify again to get 48/37.

5 0

3 years ago

Change the following decimal numbers to percents. .25 .278 2.9 3.0 0.67

umka2103 [35]

25=2,500, 278= 27800%, 2.9=290, 3.0=300, 0.67= 67

3 0

3 years ago

Read 2 more answers

Find the volume of the given solid region in the first octant bounded by the plane 9z+15y+15z=45 and the coordinate planes, usi

dem82 [27]

First,

$9x+15y+15z=45\implies 3x+5y+5z=15$

The volume is given by the integral (one of 6 possible combinations),

$\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}$

3 0

3 years ago

Given the points A(-10, -4) and B(14, 4), find the coordinates of the point P on the directed line segment AB that partitions AB

anastassius [24]

Answer:

P(5, 1)

Step-by-step explanation:

Segment AB is to be partitioned in a ratio of 5:3. That means the ratio of the lengths of AP to PB is 5:3. We need to find the ratio of the lengths of AP to AB.

AP/PB = 5/3

By algebra:

PB/AP = 3/5

By a rule of proportions:

(PB + AP)/AP = (3 + 5)/5

PB + AP = AP + PB = AB

AB/AP = 8/5

AP/AB = 5/8

The first part of the segment is 5/8 of the length of the segment, and the second part of the segment has length of 3/8 of the length of segment AB.

Point P is located 5/8 of the distance from point A to point B. The x-coordinate of point P is 5/8 of the difference in x-coordinates added to the x-coordinate of point A. The y-coordinate of point P is 5/8 of the difference in y-coordinates added to the y-coordinate of point A.

x-coordinate:

difference in coordinates: |14 - (-10)| = |14 + 10| = 24

5/8 of 24 = 5/8 * 24 = 15

Add 15 to the x-coordinate of point A: -10 + 15 = 5

x-coordinate of point P: 5

y-coordinate:

difference in coordinates: |4 - (-4)| = |4 + 4| = 8

5/8 of 8 = 5/8 * 8 = 5

Add 5 to the y-coordinate of point A: -4 + 5 = 1

y-coordinate of point P: 1

Answer: P(5, 1)

3 0

3 years ago