Answer:
The equation is [tex]t(n) = -4 + 4(n-1)[/tex]
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same.
The general equation for an arithmetic sequence is:
[tex]t(n) = t(1) + d(n-1)[/tex]
Taking the mth term as reference, the equation can be written as:
[tex]t(n) = t(m) + d(n-m)[/tex]
t(4) = 8 and t(10) = 32
The common difference can be found:
[tex]t(n) = t(m) + d(n-m)[/tex]
[tex]t(10) = t(4) + d(10-4)[/tex]
[tex]6d = 24[/tex]
[tex]d = \frac{24}{6} = 4[/tex]
So
[tex]t(n) = t(1) + 4(n-1)[/tex]
Finding the first term:
[tex]t(4) = t(1) + 4(n-1)[/tex]
So
[tex]t(1) = t(4) - 12 = 8 - 12 = -4[/tex]
So
The equation is [tex]t(n) = -4 + 4(n-1)[/tex]
