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?

Find the sum of the following arithmetic sequences for the number of terms indicated.

11. 10, 20, 30, 40, .. to 15 terms
12. 7, 11, 15, 19, ... to 20 terms
13. 14, 8, 2, -4, ... to 10 terms
14. w, 2w + 3, 3w + 6, 4w + 9, ... to 35 terms
15. 3.6, 5.7, 7.8, 9.9, .. to 27 terms
16. -2, ..., -311 for 104 terms
17. 200, ..., 25, 0 for 9 terms

Find a formula for the sum of the first n terms of the arithmetic sequences below:

18. 15, 20, 25, 30, ...
19. .2, 5, 8, 11, ...
20. 5, 1, -3, -7, ...

21. Find the sum of the first 100 terms of an arithmetic sequence with a first term of 20, a common difference of 4

22. An arithmetic sequence has a first term of 6. 
The sum of the first 10 terms is 262.5
Find the common difference.

.

23. A politician estimates that the number of handshakes he does each day before an election is increasing by about 10 per day.

On the first day of the election campaign he shakes the hands of 45 people.

How many hands will he have shaken altogether by the time of the election 30 days later?

 

 

24. The first term of an arithmetic sequence is 6 and the common difference is 4. How many terms must be added together until the sum of the terms is equal to 510?

25. A new bank began operating and in order to attract customers made a special offer of no fees for transactions. The bank set a goal of having 20 000 accounts by the end of the first year (52 weeks). At the end of the first week it had 536 accounts.

The table shows the weekly increase in the number of accounts for some of the weeks in the first year of the bank's operation.

Week
1
2
3
4
5
...
34
35
...
Increase in the number of accounts
536
527
519
512
504
...
272
264
...

a. An arithmetic sequence can be used to model the weekly increase in the number of accounts.

(i) Justify the use of an arithmetic model.

(ii) State the values of the parameters for a suitable arithmetic model.

b. Using your arithmetic model, estimate the increase in the number of accounts in week 52.

c. Will the bank reach its goal of having 20 000 accounts by the end of the first year? Justify your answer mathematically.