Geometric Series Practice Problems

Once you have solved the problems on paper, click the ANSWER button to verify that you have answered the questions correctly.

For your convenience, here’s the geometric series formula:

Problem 1: Find the sum of the first nine (9) terms of the geometric series if ${a_1} = 1$ and $r=2$ .

Answer

$511$

Problem 2: Find the sum of the first ten (10) terms of the geometric series if ${a_1} = 4$ and $r = {\large- {1 \over 2}}$ .

Answer

$\Large{{341} \over {128}}$

Problem 3: Find the sum of the first eight (8) terms of the geometric sequence.

$- 1,2, - 4,\dots$

Answer

$85$

Problem 4: Find the sum of the first six (6) terms of the geometric sequence.

$18,6,2,\dots$

Answer

$\Large{{728} \over {27}}$

Problem 5: Find the sum of the first seven (7) terms of the geometric series

$2 + 8 + 32 + \dots$

Answer

$10,922$

Problem 6: Find the sum of the first six (6) terms of the geometric series.

$- 6 + 4 - {8 \over 3} + …$

Answer

$- {{266} \over {81}}$

Problem 7: Find the sum of the geometric series below.

$1 + 4 + 16 + \dots + 1024$

Answer

$1,365$

Problem 8: Find the sum of the geometric series below.

$- 3 + 6 - 12 + \dots - 768$

Answer

$-513$

Problem 9: Evaluate the given geometric series.

${\sum\limits_{n = 1}^6 {2\left( {{1 \over 2}} \right)} ^{n - 1}}$

Answer

$\Large{{63} \over {16}}$

Problem 10: Evaluate the given geometric series.

${\sum\limits_{n = 1}^7 {64\left( { - {1 \over 4}} \right)} ^{n - 1}}$

Answer

$\Large{{3,277} \over {64}}$