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.