The first term of a linear sequence is 3 and the 8 term is 31. Find the common difference
Can't get any easier!
a = 3
a+7d = 31
replace a with 3 and solve for d
Four(4)
To find the common difference of a linear sequence, we need to observe the pattern in the sequence using the given information.
In this case, we know that the first term (usually denoted as a₁) is 3, and the eighth term (usually denoted as a₈) is 31.
We can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
Where:
aₙ is the nth term
a₁ is the first term
n is the position of the term
d is the common difference
Since we want to find the common difference, we can set up two equations using the information given:
a₁ = 3
a₈ = 31
Plugging these values into the formula:
a₈ = a₁ + (8 - 1)d
31 = 3 + 7d
Simplifying the equation:
31 = 3 + 7d
28 = 7d
d = 28/7
d = 4
Therefore, the common difference of the linear sequence is 4.