Question

I’m so confused on this. My teacher didn’t do an example of this in class for us. How do I do this?

For the sequence, describe the pattern, write the next term, and write a rule for the nth term.

17) -4, 8, -12, 16, ...

20) 2/3, 4/4, 6/5, 8/6, ...

23) 3.1, 3.8, 4.5, 5.2, ...

Answer 1

Explanation:

The sum of a number and the next the result is is alternating 4 an -4

(-4) +8 = 4

8+(-12) = -4

(-12) + 16 = 4

17)

20)Numerator is increased by 2 Numerator is increased by 1

9th is 18/11 (If 2/3 is considered the first)

9th is 16/10 if 1/1 is considered first)

The sum The sum of each fraction is 3 more than the sum of the previous fraction

2+3 = 5

4+4 = 8 (5+3)

6+5=11 (8+3)

8+6=14 (11+3)......

23)

The next number is 0.7 more than the previous number

5.2/4.5=0.7

4.5/3.8=0.7

3.8/3.1=0.7

Answer 2

See step-by-step explanation.

Explanation:

17)

• The base number increases with four every term and is alternating positive and negative.

• The next term is -20

• 
  `T(n)=4n*(-1)^(n)`

20)

• The denominator increases with 1 every term, starting at 2 for n=0. The Numerator id a multiple of two
• The next term is
  `(10)/(7)`
• 
  `T(n)=(2n)/(2+n)`

23)

• The function follows a straight line function, being increased by 0.7 at each term.
• The next term is 5.9
• 
  `T(n)=2.4+0.7n`