SOLUTION: For a geometric sequence with {{{r=1.5}}} and {{{S[5]=92.3125}}}. Find {{{S[10]}}}

Question 172798: For a geometric sequence with and . Find
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: is the 5th partial sum of the geometric sequence. To find the 5th partial sum, we use the value (since we start at ) and use the formula

Since we know that , this means that

Replace the left side with 92.3125

Plug in and

Combine like terms.

Raise 1.5 to the 5th power to get 7.59375

Combine like terms.

Divide

Divide both sides by 13.1875 to isolate "a"

Divide

So we find that (which is the first term)

Now to find , we will use

Start with the right side of the formula

Plug in , , and

Combine like terms.

Raise 1.5 to the 10th power to get 57.665 (this is approximate)

Combine like terms.

Multiply

Divide

So the tenth partial sum is approximately . This means that

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