Find the 6th term of the arithmetic sequence given an = an-1 + 8, given a1 = -20

Question

I need some help, my class is not really working to help me being online and the notes that I'm given do not match with the work assigned.

Answer 1

If the first term is -20 and each successive term is gotten by adding 8 all you need to do is add 8 to a₁ five times to get a₆.

 

Does that make sense to you?

Answer 2

Arithmetic sequences are sequences of numbers that change by a constant addition. It's important to stress that the sequence changes, meaning it can increase or decrease, by a constant addition. In decreasing sequences, the next term is computed by adding a constant negative quantity to the previous term. In increasing sequences, the next term is computed by adding a constant positive quantity to the previous term.

 

The general form is:

 

a_n = a₁ + (n - 1)d

 

where n is the number of terms in the sequence, a_n is the nth term in the sequence, a₁ is the first term, and d is the constant interval by which the sequence progresses.

 

If you have a₁ = -20 and d = 8, then the sixth term is:

 

a₆ = -20 + (6 - 1)8 = 20

 

If you graph an arithmetic sequence, you will get a straight line because the slope (d) is constant. The y-intercept is the first term in the sequence, and n is plotted on the x-axis.