11-8 Class notes - Sum of a finite geometric series

Homework for Wednesday 11-9:  page 89, items a, b, c.

Hints:  "a sub n" is the nth term of a sequence or series.
"a sub 1" is the first term.
"n" is how many terms to include in a partial sum.
"r" is the common ratio that multiplies a term to get the next term.

To find the nth term, use     a sub n = a sub 1 times r raised to the n-1 power.

To find the sum up to and including the nth term, use     S sub n = a sub 1 times [ (1- r^n) / (1 -r) ]
Don't forget that n is an exponent which raises r to a power.  In this formula you don't multiply by n.

If the successive terms are smaller, then r is a fraction or a decimal less than 1.  For example, if you take half of the current term to get the next term, the common ratio is 1/2.

An infinite geometric series often approaches a number as the finite sums have more and more terms.  This happens when r, the common ratio, is a fraction between -1 and 1.