nth term = (5 1/2) + (n - 1) * (3/2), determine the first 10 terms.
To find the first 10 terms of the sequence, we can use the given formula:
nth term = (5 1/2) + (n - 1) * (3/2)
Replacing n with each value from 1 to 10, we can calculate the terms:
1st term (n=1): (5 1/2) + (1 - 1) * (3/2) = 5 1/2
2nd term (n=2): (5 1/2) + (2 - 1) * (3/2) = 9
3rd term (n=3): (5 1/2) + (3 - 1) * (3/2) = 12 1/2
4th term (n=4): (5 1/2) + (4 - 1) * (3/2) = 16
5th term (n=5): (5 1/2) + (5 - 1) * (3/2) = 19 1/2
6th term (n=6): (5 1/2) + (6 - 1) * (3/2) = 23
7th term (n=7): (5 1/2) + (7 - 1) * (3/2) = 26 1/2
8th term (n=8): (5 1/2) + (8 - 1) * (3/2) = 30
9th term (n=9): (5 1/2) + (9 - 1) * (3/2) = 33 1/2
10th term (n=10): (5 1/2) + (10 - 1) * (3/2) = 37
Therefore, the first 10 terms of the sequence are:
5 1/2, 9, 12 1/2, 16, 19 1/2, 23, 26 1/2, 30, 33 1/2, 37