This document defines arithmetic sequences and means. It provides examples of arithmetic sequences and teaches how to identify them. Formulas are given for finding individual terms and the sum of terms in an arithmetic sequence. The document then provides practice problems for students to find individual terms, sums of sequences, and to insert arithmetic means between given numbers.

1. ARITHMETIC
SEQUENCE

2. Objectives:
>Define arithmetic
sequence,
>Define arithmetic means,
>Find the arithmetic
means

3. Arithmetic Sequence
> is a sequence where every
term after the first is
obtained by adding a
constant called the COMMON
DIFFERENCE.

4. Examples
1, 4, 7, 10, 13, 16, 19,...
8, 6, 4, 2, 0, -2, -4, ...
4, 11, 18, 25, 32, . . .

5. ARITHMETIC
SEQUENCE or
NOT

6. 5,25,45,65,85,105,125,145
1, 9, 17, 25, 33, 41, 49,57
4, 12, 36, 108, 324, 972
10, 19, 28, 37, 46, 55,64
4, 20, 100, 500, 2500

7. Arithmetic Sequence
> it is defined by the
equation given as
𝑎𝑛 = 𝑎1 + 𝑛 − 1 𝑑

8. 𝑎𝑛 = 𝑎1 + 𝑛 − 1 𝑑
Where:
an is the last term
a1 is the first term
n is the number of terms
d is the common difference

9. Arithmetic Means
>terms inserted between
two given numbers such
that the sequence will
form an arithmetic
sequence.

10. Find the arithmetic mean
between 8 and 20.

11. Find the arithmetic mean
between 3 and 7.

12. Insert 3 arithmetic means
between 18 and 30.

13. Insert 4 arithmetic means
between 3 and 48.

14. Insert 4 arithmetic means
between 7 and 37.

15. Insert 5 arithmetic means
between 18 and 54.

16. Insert 8 arithmetic means
between 8 and 116.

17. Insert 4 arithmetic means
between 5 and 35.

19. Objectives:
>Determine nth term of
an arithmetic
sequence.

20. Find the 16th term of
the sequence
1,5,9,13,…

21. Find the 20th term of
the sequence
25,23,21,19,17,…

22. In the sequence
50,45,40,35,… which
term is 5?

23. In the sequence
7,10,13,16,… which
term is 43?

24. Find the 30th, 49th,
and 103rd in the
sequence 15,23,31,39.

25. Find the 46th term of
the arithmetic
sequence
3,8,13,18,23,28,33,…

26. Given 6,13,20,27,…
Find 𝑛23.

27. Objectives:
>Determine the sum of
the terms of a given
arithmetic sequence.

28. Arithmetic Series
> A series is an
expression that
indicates the sum of
terms of sequence.

29. Arithmetic Series
𝑠𝑛 =
𝑛
2
2𝑎1 + 𝑛 − 1 𝑑
𝑠𝑛 =
𝑛
2
(𝑎1 + 𝑎𝑛)

30. Find the sum of the
first 40 terms of the
arithmetic series
2,5,8,11,…

31. Find the sum of the
first 20 terms of
arithmetic series of
𝑎1 = 5 and 𝑎20 = 62.

32. Find the sum of the
arithmetic sequence
given that:
𝑎1 = 42, 𝑎𝑛 = 146 𝑎𝑛𝑑 𝑛 = 14.

33. Find the sum of the
first 60 terms of the
following series
9,14,19,24,…

34. Given 6,13,20,27,…
Find the sum of the
first 50 terms.

35. Find the sum of the
arithmetic series
for which 𝑎1 = 34,
𝑎𝑛 = 2 and n=9.

36. Find the sum of the
terms of this
arithmetic series.
151,147,143,139,…,-5

37. Find the sum of the
following series.
1,2,3,4,5,…,48,49,50.