The document focuses on identifying arithmetic sequences, finding common differences, and determining specific terms within various sequences. It includes several examples with given sequences, asks for confirmations of arithmetic properties, and provides problems for finding terms and common differences. The structure suggests exercises aimed at students learning about arithmetic sequences and their characteristics.

1. ARITHMETIC
SEQUENCE
Finding the value of n and d
Solomon Hippocrates S. Flores
E. Rodriguez Vocational High School

2. Determine if the following sequence is arithmetic
or not. If yes, find the common difference and identify
the nextterm.
1) 4, 0, -4, -8, -12, …

3. 2) 6.6, 7.2, 7.8, 8.4, 9, …

4. 3) 7, 10, 16, 19, 25, …

6. 5) -1.2, -1.4, -1.6, -1.8, …

7. 6) 1, -6, 36, -216, 1296, …

8. 7) 1, 4, 8, 13, 19, …

9. 8) 9, 14, 19, 24, 29, …

10. 9) -8, -15, -22, -29, -36, …

11. 10) 3, 9, 27, 81, 243, …

12. Count the number of matchsticks in
each figure and record the results in a table.
Number of
squares
1 2 3 4 5 6 7 8 9
Number of
matchsticks

13. The above activity illustrates a sequence
where the difference between any two
consecutive terms is a constant. That constant is
called the common difference, d.
Given the table presented, the numbers
of matchsticks form an arithmetic sequence.
Supposed we were asked to find the specific
term for 31 matchsticks used or we are asked
to find the common difference between the
terms. Can we find a way to solve the above
stated problems?

14. Consider the following:
1. What term is 52 in the arithmetic
sequence -3, 2, 7, 12, …?
Solve for the value of n.

15. 2. In the arithmetic sequence
8, 5, 2, -1, … -34 is what term?

16. 3. Determine the term which has the
value -38 in the arithmetic sequence
7, 4, 1, -2, …?

17. Consider the following:
1. If a1 = 3, n = 27 and the last term is
107.
Solve for the common difference,
d.

18. 2. A sequence with a1 = 10 and a8 = 45.

19. 3. If the 3rd term is 11 and the
15th term is 47.

20. Solve the following.,
,
1. Which term of the arithmetic sequence 4, 1, -2, -5,
… is -29?
2. The first term of an arithmetic sequence is 2 while
the 18th term is 87. Find the common difference.
3. Which term is 68 in the arithmetic sequence 5, 12,
19, 26, …?
4. The second term of an arithmetic sequence is 24
and the fifth term is 3. Find the common difference.
5. Which term is 250 in the arithmetic sequence 10.
15, 20, 25, …?

21. Identify the
following:

22. Solve the following..,
,
1. In an arithmetic sequence 4, 7, 10, 13, … which
term has a value of 301?
2. In the sequence 2, 6, 10, … what term has a value of
106?
3. If a1 = -4 and a25 = 100, find d.
4. The 3rd term in the arithmetic sequence is -7 and
the 5th term is 20. Find the common difference.
5. Find the 29th term in the arithmetic sequence 14. 6,
-2, … .

23. Assignment
,
,
1. In the sequence 3, 7/3, 5/3, ... which
term has a value of – 27?
2. The 12th term in the arithmetic
sequence is -7 and the 25th term is 6. Find
the common difference.
3. In the sequence 2, 6, 10, 14, … which
term has a value of 286?

24. Thank you!