Geometric and Arthmetic sequence

A sequence is a list of numbers.

An arithmetic sequence is generated by adding the same number each time.

A geometric sequence is generated by multiplying the same number each time.

The formula for an arithmetic sequence is as follows:
tn=t1 + (n-1)d Where d is what is being added.
The formula for a geometric sequence is as follows:
tn=t1 x r^n-1 Where r is what is being multiplied and n is the term number.

Example 1.

Determine if the sequence is arithmetic or geometric and give the formula.

1, 4, 7, 10

This sequence is arithmetic because 3 is being added every time. So plug into your formula, tn= t1 + (n-1)d. t1 is the first term which is 1 and d which is 3.

tn= 1+ (n-1)3

tn= 1+3n-3

tn= 3n-2

Example 2.

Determine if the sequence is arithmetic or geometric and give the formula.

100, -50, 25, -12.5

This sequence is geometric because its being multiplied by -1/2. So plug into your formula, tn= t1 x r^n-1. T1 is the first term which is 100 and r is -1/2.

tn= 100 x (-1/2)^n-1

tn=100 x (-1/2)^n x (-1/2)^-1

tn= 100 x (-1/2)^n x 2

tn= 200 x (-1/2)^n