What is the rule to find the nth term in a multiplication sequence?

This is my rule to find the nth term rule for sequences like:
1,2,4,8,16,32,64
10,15, 22.5, 33.75, 50.63
1,4,16,64

First term x ((the method to get from one term to another) ^ (position-1))
The rule works but how is it simplified?
Does the rule work for all multiplication sequences??
Thanks

These are called ‘Geometric Series’ or ‘Geometric Sequences’

the formula is usually written

Tn = ar^(n-1)

where Tn is the VALUE of the Nth term
a = first term
r = the common ratio (the number you are multiplying by)
n = the position in the series

The rule can’t really be simplified past this, and yes, it does work for all Geometric Series.

3 Responses to “What is the rule to find the nth term in a multiplication sequence?”

  1. ? Says:

    These are called ‘Geometric Series’ or ‘Geometric Sequences’

    the formula is usually written

    Tn = ar^(n-1)

    where Tn is the VALUE of the Nth term
    a = first term
    r = the common ratio (the number you are multiplying by)
    n = the position in the series

    The rule can’t really be simplified past this, and yes, it does work for all Geometric Series.
    References :

  2. Ansis Says:

    Yes, it does. How could it possibly get simpler than that?
    References :

  3. Student S Says:

    the nth term for a gerometric progression sequence is

    a * r ^(n-1)

    where a is the first term and and r is the ratio.

    so for the first example:
    a=1 and r = 2/1=2

    in the second example
    a=10 and r =15/10=1.5

    in the third example:
    a=1 and r =4/1=4
    References :

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