1.
here are the first two terms of some different arithmetic sequences:
a. -2,4
b. 11, 111
c. 5, 7.5
d. 5,-4
what are the next three terms of each sequence?

a. 10, 16

b. 211, 311

c. 10 , 12.5

d. -13, -22

Step-by-step explanation:

In an arithmetic sequence, there is a constant difference, which is the difference between a term and the previous term. We find the constant different for each sequence, and we add it to the second term to find the third term. Then we add the constant difference to the third term to find the fourth term.

a.

4 - (-2) = 6

3rd term: 4 + 6 = 10

4th term: 10 + 6 = 16

b.

111 - 11 = 100

3rd term: 111 + 100 = 211

4th term: 211 + 100 = 311

c.

7.5 - 5 = 2.5

3rd term: 7.5 + 2.5 = 10

4th term: 10 + 2.5 = 12.5

d.

-4 - 5 = -9

3rd term: -4 + (-9) = -13

4th term: -13 + (-9) = -22

infinitely many solutions

step-by-step explanation:

we have been given the equation;

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

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

3

step-by-step explanation: