Transcript Arithmetic Sequences Finding the nth Term
Arithmetic Sequences Finding the nth Term
Arithmetic Sequences
• • A pattern where all numbers are related by the same common difference.
• The common difference must be an addition or subtraction constant.
• The common difference can be used to predict future numbers in the pattern.
Ex. 4, 7, 10, 13, ___, ___, ___ The common difference in this pattern is
+3
. Based on this information, you can say that the next 3 terms will be
16, 19, and 22
.
Ex. -1, -5, -9, ___, ___, ___ The common difference in this pattern is
-4
. Based on this information, you can say that the next 3 terms will be
-13, -17, and -21
.
Finding the nth Term
• If you want to find a term in an arithmetic sequence that is far into the pattern, there is a formula to use.
a n = a 1 + (n – 1)(d) a n =
the answer term you are looking for in the sequence
a 1 =
the first term in the sequence
n =
the ordinal number term you are looking for in the sequence
d =
the common difference Ex. 23, 18, 13, 8, … find the 63 rd term
a n = 23 + (63 – 1)(-5) a n = 23 + 62(-5) a n = 23 + (-310) = -287
Practice Problems
1.
11, 13, 15, 17, … Find the 85 th term 2.
25, 22, 19, 16, … Find the 50 th term 3. a 1 = -15 d = +4 Find the 71 st term 4. a n = 255 d = +3 a 1 = 36 Find n