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Exercises for Question Type 1: Finding the sum to infinity of a given sequence - IB | RevisionDojo

Question 1

Given that the sum to infinity of a geometric series is $20$ and its first term is $5$ , find the common ratio $r$ .

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Question 2

Calculate the sum to infinity of the combined series

$6 + \frac{3}{2} + \frac{3}{8} + \dots - \left(2 + 1 + \frac{1}{2} + \dots\right)$

Calculate the sum to infinity.

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Question 3

This question requires calculating the sum to infinity of a geometric sequence given its general term formula.

Find the sum to infinity of the geometric sequence defined by $u_n = 2 \cdot (0.8)^{n-1}$ .

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Question 4

Calculate the sum to infinity of the series $3 + \frac{3}{2} + \frac{3}{4} + \frac{3}{8} + \dots$ .

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Question 5

Determine the sum to infinity of the geometric sequence with first term $u_1=12$ and common ratio $r=\frac{3}{4}$ .

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Question 6

The question tests the ability to identify the parameters of an infinite geometric sequence and apply the sum to infinity formula to show a given result.

Show that the infinite sum of the sequence $7, \tfrac{7}{4}, \tfrac{7}{16}, \dots$ equals $\tfrac{28}{3}$ .

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Question 7

Find the sum to infinity of the sequence $8, -4, 2, -1, \dots$ .

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Question 8

A geometric series has common ratio $r=\frac{2}{5}$ and sum to infinity $15$ . Find its first term.

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Question 9

This question assesses the ability to calculate the sum to infinity of a geometric sequence using the appropriate formula and verifying the condition for convergence.

Calculate the sum to infinity of the geometric sequence with first term $u_1 = 5$ and common ratio $r = \frac{1}{3}$ .

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Question 10

Given that $\displaystyle \sum_{n=1}^\infty u_n = 30$ and the common ratio $r$ satisfies $\frac{1}{r} + 1 = 5$ , find $u_1$ .

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Question Type 1: Finding the sum to infinity of a given sequence Exercises