## Arithmetic Sequences Exercise

1. State whether the following sequences are arithmetic and if they are find the common differences:

a. 10, 20, 30, 40, ...
b. 7, 11, 15, 19, ...
c. 2, 4, 8, 16, ...
d. 14, 8, 2, -4, ...
e. w, 2w + 3, 3w + 6, 4w + 9, ...
f. 3.6, 5.7, 7.8, 9.9, ...
g. p + 1, p, p − 1, p − 2, ...

2. For each of the sequences above which are arithmetic, find the next two terms.

3. Find the term indicated for each of the following arithmetic sequences.

a. 2, 7, 12, 17, ... find the 15th term.
b. 2.5, 5, 7.5, 10, ... find the 20th term.
c. -2, -5, -8, -11, ... find the 10th term.
d. 200, 175, 150, 125, ...find the 30th term.
e. -4, -1, 2, 5, ... find the 100th term.
f. √5, 3√5, 5√5, 7√5, ... find the 9th term.
g. z, 3z − 2, 5z − 4, 7z − 6, ... find the 21st term.

4. Find the n th (general term) for the sequences:

a. 15, 20, 25, 30, ...
b. 2, 5, 8, 11, ...
c. 5, 1, -3, -7, ...
d. q, 3q, 5q, 7q, ...
e. 18, 10, 2, -6, ...
f. 4.5, 9.1, 13.7, 18.3, ...
g. 1010, 990, 970, 950, ...

5. If the 6th term of an arithmetic sequence is 18 and the 16th term is 48, find the common difference and the first term and thus list the first four terms of the sequence.

6. If the 5th term of an arithmetic sequence is 7.5 and the 12th term is 3.3, find the common difference and the first term and thus list the first four terms of the sequence.

7. How many multiples of 4 are there between 334 and 982?

8. Which term of the sequence 6, 9, 12, 15, ... is equal to 147?

9. Which term of the sequence 100, 95, 90, 85, ... is equal to -100?

 10. A runner runs 5.6 km on the first day of training. She increases her training by 0.2 km each day. How far will she be running by the 30th day of training?