The first terme of a linear sequence is 3 and the 8th term is 31.find the common difference

by definition

term8 = a + 7d
sub in our data
3 + 7d = 31
7d = 28
d = 4

To find the common difference of a linear sequence, we can use the formula for the nth term:

nth term = first term + (n - 1) * common difference

In this case, the first term is 3 and the 8th term is 31, so we can substitute these values into the formula:

31 = 3 + (8 - 1) * common difference

Simplifying:

31 = 3 + 7 * common difference

Now we can isolate the common difference by subtracting 3 from both sides:

28 = 7 * common difference

Finally, divide both sides by 7 to solve for the common difference:

common difference = 28 / 7

Therefore, the common difference is 4.