the first of a linear sequence is 3 and the 8th term is 31 find the common difference
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3, 3+d, 3+2d , 3+3d ....... 3+7d
3+7d = 31
To find the common difference in a linear sequence, we need to use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
Here, the given information is:
First term (a1) = 3
8th term (a8) = 31
Let's substitute these values into the formula to form two equations:
a1 = 3
a8 = 3 + (8 - 1) * d (where d is the common difference)
By substituting a1 and a8, we can solve for d:
3 + (8 - 1) * d = 31
3 + 7d = 31
7d = 31 - 3
7d = 28
d = 28 / 7
d = 4
Therefore, the common difference in this linear sequence is 4.