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The name of a sequence where the values are added or subtracted by the same constant from one term to the next to find the next term of the sequence.
Arithmetic
The name of a sequence where the values are multiplied by a constant from one term to the next to find the next term of the sequence.
Geometric
recursive rule
18, 25, 32, 39, 46, ......
f(1)=18, f(n)=f(n-1)+7
The sum of the series for n=1 to n=6
sum(2n-5)
12
The name of the value that is added from one term to the next to get the next value in an Arithmetic sequence.
Common Differece
The name of the value that is mulitiplied from one term to the next to get the next value in a Geometric sequence.
Common Ratio
recursive rule
100, 50, 25, 12.5, 6.25, ......
f(1)=100, f(n)=f(n-1)x(0.5)
The value of the 4th term of the series
sum2(3)^n
162
65, 73, 81, 89, 97, ......
8
The common ratio
540, 135, 33.75, 8.4375, .....
0.25
recursive rule
98304, 12288, 1536, 192, 24, ......
f(1)=98304, f(n)=f(n-1)x(1/8)
The sum of the series for n=3 to n=8
sum-6n+10
-138
The recursive rule
175, 152, 129, 106, 83, ....
f(1)=175 , f(n)=f(n-1)-23
The recursive rule
8, -24, 72, -216, 648, ......
f(1)=8 , f(n)=f(n-1) x (-3)
The 1st 5 terms of the sequence?
f(1)=5, f(n)=f(n-1)-12
5, -7, -19, -31, -43
The sum of the series for n=2 to n=10
sum4(-2)^(n-1)
-1368
The explicit rule
-47, -33, -19, -5, 9, ........
f(n)=14n-61
The explicit rule
14 , 154 , 1694 , 18,634 , ......
f(n)=14(11)^(n-1) or f(n)=14/11(11)^n
The 1st 5 terms of the sequence.
f(0)=4, f(n)=f(n-1)x(-4)
-16, 64, -256, 1024, -4096
The sum of the series for n=1 to n=5
sum25n+6
405