# Lesson Worksheet: Sum of a Finite Geometric Sequence Mathematics • 10th Grade

In this worksheet, we will practice calculating calculate the sum of the terms in a geometric sequence with a finite number of terms.

Q1:

We can find a formula for the sum of a geometric series. Consider the series

Multiply the expression for by , the common ratio.

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So, we have and

The right-hand sides of the equations are very similar. Identify the terms that do not appear on the right-hand side of both equations.

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Now, consider the subtraction

Use the answer to the previous part to simplify the subtraction .

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Factor both sides of the equation.

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Rearrange the equation to make the subject of the formula.

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Q2:

In a geometric sequence, the first term is and the common ratio is .

Find the sum of the first 3 terms of a geometric sequence with and .

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Q3:

A geometric series has a first term of 3 and a common ratio of 5. Find the sum of the first 6 terms.

Q4:

Find the sum of the geometric sequence .

Q5:

Find the sum of the first 7 terms of a geometric sequence given and .

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Q6:

Find the number of terms in the geometric sequence given the first term is 21, the last term is , and the sum of all the terms is .

Q7:

Find the geometric sequence given the sum of all the terms is 3,339, the last term is 1,696, and the common ratio is 2.

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Q8:

Fill in the blank: The number of terms of a geometric sequence whose first term is 729, last term is 1, and sum of all terms is 1,093 is .

Q9:

Find the geometric sequence and the sum of the first six terms given the second term is four times the fourth one, the sum of the fourth and seventh terms is 2 and all terms are positive.

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Q10:

Find the geometric sequence and the sum of the first five terms given the sum of the first three terms is 1 and the sum of the next three terms is 27.

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