To find the equation for the nth term of the given arithmetic sequence, we first need to determine the first term and the common difference.
The first term (a1) of the sequence is 9. To find the common difference (d), we subtract the first term from the second term:
d = 11 – 9 = 2
This common difference remains constant throughout the sequence. The nth term (an) of an arithmetic sequence can be expressed with the formula:
an = a1 + (n – 1) * d
Now, substituting the values we have:
an = 9 + (n – 1) * 2
This simplifies to:
an = 9 + 2n – 2
an = 2n + 7
Thus, the equation for the nth term of the sequence 9, 11, 13, 15 is an = 2n + 7.