the 1st term of a linear sequence is 3 and the 8th term is 31 find the common difference
7 differences equal (31 - 3)
To find the common difference in a linear sequence, we'll use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
Given that the first term (1st term) is 3 and the 8th term is 31, we can substitute these values into the formula:
3 + (8 - 1) * common difference = 31
Simplifying the equation, we get:
3 + 7 * common difference = 31
Now, we can subtract 3 from both sides of the equation:
7 * common difference = 28
Dividing both sides by 7, we find:
common difference = 28 / 7
Simplifying further, we get:
common difference = 4
Therefore, the common difference in this linear sequence is 4.