Arithmetic Sequences Practice 2 worksheet with problems on identifying, extending, and graphing arithmetic sequences.

1. Yes, the sequence is arithmetic. The common difference is 10 (24 - 14 = 10, 34 - 24 = 10).

2. The next three terms are 7/2, 9/2, and 11/2. The common difference is 1 (3/2 - 1/2 = 1, 5/2 - 3/2 = 1).

5. Recursive rule: a(1) = 3.2; a(n) = a(n-1) + 1.5 for n > 1.

6. Explicit rule: a(n) = -8n - 1. To find a(42), substitute n=42: a(42) = -8(42) - 1 = -336 - 1 = -337.

7. Explicit rule: a(n) = 2n - 1. To find a(81), substitute n=81: a(81) = 2(81) - 1 = 162 - 1 = 161.

8. Recursive rule: a(1) = 24; a(n) = a(n-1) + 6 for n > 1. To find a(7): a(2)=30, a(3)=36, a(4)=42, a(5)=48, a(6)=54, a(7)=60.

9. Complete the table:
n: 1, 2, 3, 4, 5, 6, 7, 8
a(n): -8, -5, -2, 1, 4, 7, 10, 13
Graphing these points (n, a(n)) will show they lie on a straight line with a positive slope. This indicates a linear relationship, which is characteristic of an arithmetic sequence.