Sequence and Arithmetic Sequence Made by: Grade 10-Newton of Caloocan National Science and Technology High School

1. Panganiban E.J., Icatlo A.J., Susano G., De Leon M., Neric A.R.
10 Newton
A.Y. 2015-2016

2. Sequence
a sequence is an ordered
collection of objects in which
repetitions are allowed. Like a set,
it contains members (also
calledelements,orterms).

3. In Math, a sequence Is a
function whose domain is
the finite set {1, 2, 3,…, n}
or the infinite set {1, 2, 3,…}

4. Arithmetic
Sequences
Geometric
Sequences
Other types
of sequences
Finding the next term
Finding the nth term
Finding the Arithmetic/Geometric Means
Finding the Sum of the First n Terms
Solving Real-Life Problems

5. EXAMPLES
By following the pattern, write the
next three terms in the sequence
1.) 3, 5, 7, ___, ___, ___
2.) 3, 1, -1, ___, ___, ___
3.) 1/4, 1/9, 1/16, ___,
___, ___
4.) x, x+y, x+2y, ___, ___,
___
5.) 3, 6, 9, ___, ___, ___

6. 1.) 3, 5, 7, 9, 11, 13
2.) 3, 1, -1, -5, -7, -9
3.) 1/4, 1/9, 1/16, 1/25,
1/36, 1/49
4.) x, x+y, x+2y, x+3y,
x+4y, x+5y
5.) 3, 6, 9, 12, 15, 18
Answers:

7. Arithmetic
Sequence

8. A sequence where each
term after the first is
obtained by adding the
same constant which is
called the common
difference
Arithmetic Sequence

9. Terms between two
nonconsecutive terms of an
arithmetic sequence
an - ak
n - k

10. Examples
{5, 8, 11, 14, 17, 20, 23}
Where a1 = 5, a7 = 23, and d = 3

11. {50, 44, 38, 32,…}
Where a1 = 50, a4 = 32, and d = -6

12. The first term of an arithmetic
sequence is equal to 200 and the
common difference is equal to -10.
Find the value of the 20th term.
a20 = 200 + (20 - 1) (-10)
a20 = 200 - 190
a20 = 10
an = a1 + (n - 1) d

13. If a1 = 4, a4 = 13, what are
the values of a2 and a3?
an - ak
n - kd =
13 - 4
4 - 1d =
d = 3
4 , 7 , 10 , 13

14. Let’s Try!
1.) 3, 1, -1, … the 21st term
2.) 14, 6, -2, …the 29th term
3.) 18th term of the arithmetic
sequence if a1 = 25 and d=2

15. Answers:
1.) 3, 1, -1, … the 21st term
an = a1 + (n - 1) d
a21 = 3 + (21-1)(-2)
a21 = 3 + (-40)
a21 = -37

16. Answers:
2.) 14, 6, -2, …the 29th term
an = a1 + (n - 1) d
a29 = 14 + (29 - 1)(-8)
a29 = 14 + (-224)
a29 = -210

17. Answers:
3.) 18th term of the arithmetic
sequence if a1 = 25 and d=2
an = a1 + (n - 1) d
a18 = 25 + (18-1)(-2)
a21 = 25 + (-34)
a21 = -9