ARITHMETIC SEQUENCE (AP) GEOMETRIC SEQUENCE (GP)
Linear number patterns Exponential number patterns
Terminology common to both AP and GP:
a is the first term of the sequence so a = T1
n is the number of the term and gives its position
Tn is the general term and gives the value of the term in the nth position
d = the common difference between successive r = the common ratio of successive terms
terms
How to determine the value of the common How to determine the value of the common
difference: ratio:
d = T3 – T2 = T2 – T1 T3 T2
r= =
T2 T1
How to determine the general term:
T1 = a T1 = a
T2 = a + d T2 = a x r
T3 = a + d + d = a + 2d T3 = a x r x r = ar²
T4 = a +3d T4 = ar³
T5 = a + 4d T5 = ar⁴
etc… etc…
T10 = a + 9d T10 = ar⁹
General term: Tn = a+(n-1)d General term: Tn = arⁿ⁻ⁱ
Linear number patterns Exponential number patterns
Terminology common to both AP and GP:
a is the first term of the sequence so a = T1
n is the number of the term and gives its position
Tn is the general term and gives the value of the term in the nth position
d = the common difference between successive r = the common ratio of successive terms
terms
How to determine the value of the common How to determine the value of the common
difference: ratio:
d = T3 – T2 = T2 – T1 T3 T2
r= =
T2 T1
How to determine the general term:
T1 = a T1 = a
T2 = a + d T2 = a x r
T3 = a + d + d = a + 2d T3 = a x r x r = ar²
T4 = a +3d T4 = ar³
T5 = a + 4d T5 = ar⁴
etc… etc…
T10 = a + 9d T10 = ar⁹
General term: Tn = a+(n-1)d General term: Tn = arⁿ⁻ⁱ
