To find the equation for the nth term of the arithmetic sequence 20, 16, 12, 8, we first identify the common characteristics of the sequence:
- First Term (a): The first term of the sequence (denoted as a) is 20.
- Common Difference (d): The common difference (denoted as d) can be calculated by subtracting the second term from the first term: 16 – 20 = -4.
With that information, we can use the formula for the nth term of an arithmetic sequence, which is:
T(n) = a + (n – 1) * d
Substituting the values we identified:
- a = 20
- d = -4
Therefore, the formula becomes:
T(n) = 20 + (n – 1) * (-4)
Simplifying this further:
T(n) = 20 – 4(n – 1)
Now, distribute -4:
T(n) = 20 – 4n + 4
Combining like terms gives:
T(n) = 24 – 4n
Thus, the equation for the nth term of the arithmetic sequence 20, 16, 12, 8 is:
T(n) = 24 – 4n