SOLUTION: Find the sum of the terms of a geometric sequence where the first term is 4, the last term is 324, and the common ratio is 3. U

Question 1044698: Find the sum of the terms of a geometric sequence where the first term is 4, the last term is 324, and the common ratio is 3.
U
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

To find the sum of a certain number of terms of a geometric sequence:

where is the sum of terms (nth partial sum),
is the first term, is the common ratio.
if given the first term is , the last term is , and the common ratio is than we need first to find what number is the last term:
To find any term of a geometric sequence:

where a[1] is the first term of the sequence, is the common ratio, is the number of the term to find

.........since base same, exponents must be same too, so we have

-> so, your sequence have terms
than the sum will be:

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
On geometric progressions, see the lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

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