The first term of an arithmetic sequence is -4. the 8th term is 10. what is the common difference?

  2

Step-by-step explanation:

The general term of an arithmetic sequence is given by the explicit formula ...

  an = a1 +d(n -1)

The first term is a1 = -4, and the 8th term is a8 = 10. Using these numbers in the formula, we find ...

  a8 = a1 +d(8 -1) . . . . put n=8 into the formula

  10 = -4 + 7d . . . . . . . fill in the other known values

  14 = 7d . . . . . . . . . . . add 4

  2 = d  . . . . . . . . . . . . . divide by 7

The common difference is 2.

You may have noticed that the difference between the first and eighth terms is 8-1 = 7 times the common difference. And, our solution is ...

  d = (10 -(-4))/7 = 2

12/11c

or

12

c

11

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square