Precalculus Examples

18 , 6 , 2
Step 1
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 13 gives the next term. In other words, an=a1rn-1.
Geometric Sequence: r=13
Step 2
This is the form of a geometric sequence.
an=a1rn-1
Step 3
Substitute in the values of a1=18 and r=13.
an=18(13)n-1
Step 4
Apply the product rule to 13.
an=181n-13n-1
Step 5
One to any power is one.
an=1813n-1
Step 6
Combine 18 and 13n-1.
an=183n-1
Step 7
Substitute in the value of n to find the nth term.
a4=183(4)-1
Step 8
Simplify the denominator.
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Step 8.1
Subtract 1 from 4.
a4=1833
Step 8.2
Raise 3 to the power of 3.
a4=1827
a4=1827
Step 9
Cancel the common factor of 18 and 27.
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Step 9.1
Factor 9 out of 18.
a4=9(2)27
Step 9.2
Cancel the common factors.
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Step 9.2.1
Factor 9 out of 27.
a4=9293
Step 9.2.2
Cancel the common factor.
a4=9293
Step 9.2.3
Rewrite the expression.
a4=23
a4=23
a4=23
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 [x2  12  π  xdx ] 
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