Sequence Patterns in Sequences General Term/Rule For more instructional resources, CLICK me here! 👇👇👇 https://tinyurl.com/y9muob6q LIKE and FOLLOW me here! 👍👍👍 https://tinyurl.com/ycjp8r7u https://tinyurl.com/ybo27k2u

1. Grade 10 – Mathematics
Quarter I
PATTERNS IN SEQUENCES

2. OBJECTIVES:
• define sequence, finite and infinite
sequence;
• list the next few terms given several
consecutive terms of a sequence; and
• derive a mathematical expression
(rule) for generating the sequence by
pattern searching.

3. ACTIVITY
1. A, D, G, J, ____, ____, ____
2. 1, 3, 5, 7, ____, ____, ___
3. 1, 4, 9, 16, 25, ____, ____, ____
4. 5, 15, 25, 35, ____, ____, ____
5. 1, 3, 6, 10, ____, ____, ____
M P S
9 1311
36 49 64
45 55 65
15 21 28

4. A sequence is a function whose
domain is the set of positive
integers. It also means an ordered
list of numbers.

5. A sequence is infinite if its domain is the
set of positive integers without a last term, {1,
2, 3, 4, 5, ...}. The three dots show that the
sequence goes on and on indefinitely.
A sequence is finite if its domain is the set
of positive integers {1, 2, 3, 4, 5, …, n} which
has a last term, n.

6. Each number in a sequence is
called a term.
Example:
5, 15, 25, 35, 45.
1st
2nd
3rd
4th
5th
5 termsn

7. In the sequence 1, 3, 6, 10, 15,… we can
denote the terms as follows:
𝑎1 = 1 𝑎2 = 3 𝑎5 = 15𝑎4 = 10𝑎3 = 6
Rule: 𝒂 𝒏 =
𝒏
𝟐
(𝒏 + 𝟏)
𝑎1 =
1
2
(1 + 1) = 1
𝑎2 =
2
2
2 + 1 = 3
𝑎3 =
3
2
(3 + 1) = 6
𝑎4 =
4
2
4 + 1 = 10
𝑎5 =
5
2
(5 + 1) = 15
2 4
53
6

8. Find the first 5 terms of the sequence whose general term is
given by 𝒂 𝒏 = 𝒏 − 𝟑 𝒏
.
_____, _____, _____, _____, _____
1st 2nd
3rd 4th 5th
𝑎 𝑛 = 𝑛 − 3 𝑛
𝑎1 = 1 − 3 1
= −2 1
= - 2
𝑎2 = 𝑛 − 3 𝑛
𝑎2 = 2 − 3 2
= −1 2
= 1
−2 1

9. Find the first 5 terms of the sequence whose general term is
given by 𝒂 𝒏 = 𝒏 − 𝟑 𝒏
.
_____, _____, _____, _____, _____
1st 2nd
3rd 4th 5th
−2 1
𝑎 𝑛 = 𝑛 − 3 𝑛
𝑎3 = 3 − 3 3
= 0 3
= 0
𝑎 𝑛 = 𝑛 − 3 𝑛
𝑎4 = 4 − 3 4
= −1 4
= 1
0 1

10. Find the first 5 terms of the sequence whose general term is
given by 𝒂 𝒏 = 𝒏 − 𝟑 𝒏
.
_____, _____, _____, _____, _____
1st 2nd
3rd 4th 5th
−2 1 0 1
𝑎5 = 𝑛 − 3 𝑛
𝑎5 = 5 − 3 5
= 2 5
= 32
32

11. Find the first 4 terms and the 20th term of the sequence
whose general term is given by 𝒂 𝒏 =
−𝟏 𝒏
𝟐𝒏−𝟏
.
𝑎2 =
−1 2
2(2)−1
=
1
3
_____, _____, _____, _____, …, _____
1st 2nd
3rd 4th
20th
𝑎1 =
−1 1
2(1) − 1
=
−1
1
= −1
−1
1
3

12. Find the first 4 terms and the 20th term of the sequence
whose general term is given by 𝒂 𝒏 =
−𝟏 𝒏
𝟐𝒏−𝟏
.
𝑎4 =
−1 4
2(4) − 1
=
1
7
𝑎3 =
−1 3
2(3) − 1
=
−1
5
_____, _____, _____, _____, …, _____
1st 2nd
3rd 4th
20th
−1
1
3
−
1
5
1
7

13. Find the first 4 terms and the 20th term of the sequence
whose general term is given by 𝒂 𝒏 =
−𝟏 𝒏
𝟐𝒏−𝟏
.
_____, _____, _____, _____, …, _____
1st 2nd
3rd 4th
20th
−1
1
3
−
1
5
1
7
1
39
𝑎20 =
−1 20
2(20) − 1
=
1
39
−𝟏 𝒏
the general term causes
the signs of the terms
to alternate between
positive and negative

14. For each sequence, make a guess at the
general term.
1, 8, 27, 64, 125, … 𝑎 𝑛 = 𝑛3
1,
1
2
,
1
3
,
1
4
,
1
5
, … 𝑎 𝑛 =
1
𝑛
-5, 10, -15, 20, -25, … 𝑎 𝑛 = (−1) 𝑛
5𝑛

15. For each sequence, make a guess at the
general term.
1, 4, 9, 25, … 𝑎 𝑛 = 𝑛2
3, -6, 9, -12, 15, … 𝑎 𝑛 = (−1) 𝑛 − 3𝑛
-2, 4, -8, 16, … 𝑎 𝑛 = (−1) 𝑛
2 𝑛