The sequence given is 15, 12, 9, 6, which is an arithmetic sequence. In an arithmetic sequence, each term is generated by adding or subtracting a constant difference to the previous term.
To find the nth term of this sequence, we first identify the first term (a) and the common difference (d). The first term (a) is 15. To find the common difference, we can subtract the second term from the first term:
d = 12 – 15 = -3
Now that we know a = 15 and d = -3, we can use the formula for the nth term of an arithmetic sequence, which is:
T(n) = a + (n – 1)d
Substituting the values of a and d into the formula gives us:
T(n) = 15 + (n – 1)(-3)
Expanding this, we get:
T(n) = 15 – 3(n – 1)
When you simplify this further:
T(n) = 15 – 3n + 3 = 18 – 3n
Thus, the expression for the nth term of the sequence is:
T(n) = 18 – 3n