This week I'm going to do a review on 13-1, where we learned how to identify arithmetic and geometric sequences, how to find the formula for each type of sequence, and how to find an indicated term or number of terms of a sequence.
-arithmetic sequence: a sequence that is generated by adding the same number each time
-formula: tn= t1 + (n - 1)d
-goemetric sequence: a sequence that is generated by multiplying the same number each time
-formula: tn = t1 x r^n-1
*to divide, we use fractions/2 = x 1/2
Example 1: Identify the following as arithmetic or geometric.
a) 4,6,8,...
= arithmetic
b) 2,4,8,16,...
= geometric
Example 2: Find the formula for the nth term.
a) 1,4,7,10...
- arithmetic
- tn = t1 + (n - 1)d
= tn = 1 + (n -1)3
= tn = 1 + 3n - 3
= 3n-2
b) 8,4,2,1,...
- geometric
- tn = t1 x r^n-1
= tn = 8 x 2^n-1
= tn = 8 x 2^n x 2^-1
= tn = 8 x 2^n/2
= 4 x 2^n
Example 3: Find the indicated term of the arithmetic sequence.
- t1 = 15, t2 = 21, t20 = ?
- 15 + d = 21
= d = 6
- tn = t1 + (n - 1)d
= t20 = 15 + (20 - 10)6
= 15 + 120 - 6
= 129
Example 4: Find the indicated term of the geometric sequence.
- t1 = 4, t3 = 36, t7 = ?
- 4 x r x r = 36
= 4r^2 = 36
= r = 3
- tn = t1 x r^n-1
= t7 = 4 x 3^7-1
= 4 x 3^6
= 2,916
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