What does this mean and how do I solve it?

Question

The value of the 8th term is 78. The sequence is increasing by 10 each step.

 

Explicit equation:   y=10x-2

Recursive:   now= previous term + 10

 

 

 

Find the 20th term._______________

Explanation:

Answer 1

a_n = a₁ + (n - 1)d

a₁₂ = 78 + (13 - 1)10        12 differences from a₈ to a₂₀

a₁₂ = 78 + 120

a₁₂ = 198

 

The twentieth term is 198

Answer 2

In the explicit equation, x represents the nth term.  y represents the actual term.

 

So if x=8 for 8th term, then

 

y = 10(8) - 2 = 80 - 2 = 78     is the actual term.

 

 

20th term:

 

Solve for y when x=20.

 

 

 

In the recursive, you add the value that is given to you, which is 78, then add 10 to it.  Let me show you how it works.

 

 

now = previous + 10

 

now = 78 + 10 = 88   ---> value (9th term)

 

The original "previous" represented the 8th term.

 

 

now = 88 + 10 = 98    ----> value (10th term)

 

now = 98 + 10 = 108  ----->  value (11th term)

 

now = 108 + 10 = 118  ---->  value (12th term)

 

 

Continue this pattern until you get to  20th term.