Write the first four terms of the sequence 1/2,add 1/3

1 answer:

3 0

To find the first four terms of a sequence that starts with 1/2 and has a common difference of 1/3, we can start by adding 1/3 to 1/2 (because it's the common difference). The first term is 1/2 (since it's already given to us). The next term is 1/2 + the common difference, or 1/2 + 1/3 or 5/6. The next term is 5/6 + 1/3, which is 7/6. The next term is 7/6 + 1/3 = 3/2. That means that the first four terms of this sequence are 1/2, 5/6, 7/6, and 3/2.

You might be interested in

The eastbound train travels 10 miles per hour faster than the westbound train. After 2 hours, they are 232 miles apart. At what

patriot [66]

Answer:

48,58

Step-by-step explanation:

Let The speed of the west bound train be x

Let the east bound train be x+10

The speeds can be calculated as follows

2(2x+10)= 232

4x + 40= 232

4x= 232-40

4x= 192

x= 192/4

= 48

Hence the speedof the west bound train is 48

The speed of the east bound train is 48+10

= 58

8 0

2 years ago

A telephone pole has a wire to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor po

Bumek [7]

Answer:

The height of the pole is 105ft,

Step-by-step explanation:

Let us call $h$ the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is $h - 49$ .

The wire length $d$ is 14 ft longer than height $h$ , hence

$d= h+14$ .

Thus we get a right triangle with hypotenuse $d= y+14$ , perpendicular $h$ , and base $h-49$ ; therefore, the Pythagorean theorem gives

$(h-49)^2+h^2 = (h+14)^2$

which upon expanding we get:

$h^2-98h+2401 = h^2+28h+196$

further simplification gives

$h^2-126h+2205=0$ ,

which is a quadratic equation with solutions

$h =21ft\\h = 105ft.$

Since the first solution $h =21ft$ will give the triangle base length of $21ft-49ft = -28ft$ which is negative; therefore, we disregard it and pick the solution $h = 105ft$ .