Question

3. If x +4, 2x+5, and 4x +3 represent the first three terms of an arithmetic sequence, then find the

value of x. What is the fourth term?

Answer 1

To find the value of x in the arithmetic sequence, we solved the equation x + 1 = 2x - 2 to get x = 3. Then, using the common difference of 4, we found the fourth term to be 23.

Step-by-step explanation:

To find the value of x for an arithmetic sequence, we need to use the property that the difference between any two consecutive terms is constant. Given the three terms of the sequence x + 4, 2x + 5, and 4x + 3, we can set up two equations based on the common difference:

1. (2x + 5) - (x + 4) = (4x + 3) - (2x + 5)
2. x + 1 = 2x - 2

By simplifying the second equation, we isolate x:

x = 3

Having found the value of x, we can now determine the fourth term in the sequence. The common difference is the same as the difference between the second and first terms:

Common difference (d) = (2x + 5) - (x + 4)

Inserting x = 3, we get:

d = (2(3) + 5) - (3 + 4) = 11 - 7 = 4

The second term is 2x + 5, so:

Second term = 2(3) + 5 = 11

The fourth term is three times the common difference added to the second term:

Fourth term = 11 + 3(4) = 23

Answer 2

first term = initial number

second term = initial number + common difference

third term = initial number + 2(common difference)

So...

2x+5-(x+4) = common difference

4x+3-(2x+5) = also common difference

2x+5-(x+4) = x+1

4x+3-(2x+5) = 2x-2

Because x+1=2x-2 we can solve for x.

x=3

So the sequence goes... 7,11,15...

19 is the fourth term