Page 228 - Algebra 1

Math Reasoning
Write Explain the difference between a1 and a1.
Term
Term Number (n)
Sequence Pattern
Description
1st or a1
1
7
a1
2nd or a2
2
7 + 4 = 7 + (1)4
a1 + (1)d
3rd or a3
3
7 + 4 + 4 = 7 + (2)4
a1 + (2)d
4th or a4
4
7 + 4 + 4 + 4 = 7 + (3)4
a1 + (3)d
5th or a5
5
7 + 4 + 4 + 4 + 4 = 7 + 4(4)
a1 + (4)d
nth or an
n
7 + (n - 1)4
a1 +(n-1)d
Finding the nth Term of an Arithmetic Sequence
an = a1 + (n - 1)d
a1 = first term d = common difference
Example
3
Finding the nth Term in Arithmetic Sequences
a. Use the rule an the sequence.
SOLUTION
4th term:
a4 = 6 + (4 - 1)2
= 6 + (3)2 = 6 + 6
= 12
= 6 + (n - 1)2 to find the 4th and 11th terms of
11th term:
a11 = 6 + (11 - 1)2
= 6 + (10)2 = 6 + 20
= 26
b. Find the 10th term of the sequence 3, 11, 19, 27, .... SOLUTION
a1 =3andthecommondifferenced=11-3=8
an = 3 + (n - 1)8 a10 = 3 + (10 - 1)8 a10 = 75
Write the rule, substituting for a, and d. Substitute the value for n.
Simplify using the order of operations.
c. Find the 10th term of the sequence _1, _3, _5, _7, .... 4444
SOLUTION
a1 =_1 andd=_3 -_1 =_2 =_1 4 4442
an = _1 + (n - 1)_1 42
a10 = _1 + (10 - 1)_1 42
a10 = _19 4
Write the rule, substituting for a, and d. Substitute the value for n.
Simplify using the order of operations.
Lesson 34 213