What is the common difference of the sequence below?

3

Step-by-step explanation:

Givens

Start by looking at the 'distance' (number of spaces) between 1 and 10

a = 1

l = 10

n of terms = 4

L_4 = 10

a = 1

Equation

L_4 = a + (n - 1)*d

10 = 1 + (4 - 1)*d

10 - 1 = 3d

9 = 3d

9/3 = d

d = 3

So the terms you get from 1 to 10

1  4   7 10

Discussion

But we actually started at 1, not -11. Let's fill in the 3 blanks leading up to 1

-11 1

a = - 11

t = 5

L= 1

1 = - 11 + (5 - 1) d

1 = -11 + 4d                Add 11

1+ 11 = 4d

12 = 4d

12/4 = d

d = 3

Could we have done this more directly. Yes, we could have

a = - 11

t = 8       There are 8 terms in all.

L_8 = 10

L_9 = a + (n-1)d

10 = - 11 + (8-1)d

10+11 = 7d

21 = 7d

21/7 = d

d = 3