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

In this lesson, we will learn how to calculate the sum of the terms in a geometric sequence with a finite number of terms.

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17:31

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Q1:

We can find a formula for the sum of a geometric series. Consider the series 𝑆=π‘Ž+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+β‹―+π‘Žπ‘Ÿ.

Multiply the expression for π‘†οŠ by π‘Ÿ, the common ratio.

So, we have 𝑆=π‘Ž+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+β‹―+π‘Žπ‘ŸοŠοŠ¨οŠ©οŠοŠ±οŠ§ and π‘Ÿπ‘†=π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+β‹―+π‘Žπ‘Ÿ.οŠͺ

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.

Now, consider the subtraction π‘†βˆ’π‘Ÿπ‘†=ο€Ήπ‘Ž+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+β‹―+π‘Žπ‘Ÿο…βˆ’ο€Ήπ‘Žπ‘Ÿ+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+π‘Žπ‘Ÿ+β‹―+π‘Žπ‘Ÿο….οŠͺ

Use the answer to the previous part to simplify the subtraction π‘†βˆ’π‘Ÿπ‘†οŠοŠ.

Factor both sides of the equation.

Rearrange the equation to make π‘†οŠ the subject of the formula.

Q2:

In a geometric sequence, the first term is π‘Ž and the common ratio is π‘Ÿ.

Find the sum of the first 3 terms of a geometric sequence with π‘Ž=328 and π‘Ÿ=14.

Q3:

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

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