High School Mathematics - 2 3.12 Find the Term of the Sequence
Example 1:
Find a_{53} term of the arithmetic sequence with a_{1} = 5 and a_{7} = 29.
Given:
First term = a_{1} = 5 and
Seventh term = a_{7} = 29
Find: a_{53} Solution: Using the formula
a_{7} = a_{1} + 6d
29 = 5 + 6d
24 = 6d
d = 4
a_{53} = a_{1} + 52.d = 5 + 52.4 = 213
Example 2
Find the number of multiples of 9 between 30 and 901.
The first multiple of 9 in the range is 36. a_{1} = 36
The last multiple of 9 in the range is 900. a_{n} = 900
Using the formula: a_{n} = a_{1} + d(n-1)
900 = 36 + 9(n - 1) solving for n
864 = 9n - 9
873 = 9n
n = 97 Solution: There are 97 multiples in between 30 and 901
Directions: Answer the following questions. Also write at least 5 examples of your own.