Term-to-term rule

Term-to-term rule

We write the term to term rule (inductive sequence definition) as:

• u_{n+1}=ru_n
• u_1=a

r is the multiplier that the terms increase by; a is the initial term.

Position-to-term rule

The position to term rule (deductive sequence definition) for a geometric sequence is:

u_n=a\times r^{n-1}

Ratio between terms

The ratios of two consecutive terms in a geometric sequence are always equal.

That means for a sequence x,\,y,\,z,\,..., \frac yx=\frac zy