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Exercises for Question Type 1: Finding the nth term given the first term and the common ratio - IB | RevisionDojo

Question 1

An investment of $100 grows by 5% each year. Find its value after 20 years (compounded annually).

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Question 2

Find the 10th term of a geometric sequence with $u_1 = 7$ and $r = \frac{2}{3}$ .

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Question 3

Find the 5th term of a geometric sequence where $u_1 = 5$ and $r = 3$ .

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Question 4

Write an expression for the $n$ th term of a geometric sequence with first term $u_1 = 6$ and common ratio $r = 0.5$ .

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Question 5

The question requires calculating the population of a culture undergoing exponential growth (doubling) over a specific time period. This can be modeled using a geometric sequence or an exponential function.

A bacterial culture doubles every hour. If the initial population is 100, find the population after 10 hours.

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Question 6

Calculate the 4th term of a geometric sequence with $u_1 = -2$ and $r = 4$ .

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Question 7

A geometric sequence is defined by its first term $u_1$ and its common ratio $r$ . The $n^{\text{th}}$ term of a geometric sequence is given by the formula $u_n = u_1 r^{n-1}$ .

Find the 12th term of a geometric sequence with $u_1 = 3$ and $r = \frac{1}{3}$ .

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Question 8

Write an expression for the $n$ th term of a geometric sequence with first term $u_1 = 9$ and common ratio $r = -\frac{1}{3}$ .

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Question 9

Find the 6th term of a geometric sequence with first term $u_1 = 3$ and common ratio $r = 2$ .

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Question 10

Calculate the 7th term of a geometric sequence with first term $u_1 = -3$ and common ratio $r = -\frac{1}{2}$ .

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Question 11

Geometric sequences and their terms.

Determine the 5th term of a geometric sequence with $u_1 = 8$ and $r = -1.5$ .

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Question 12

Find the 4th term of a geometric sequence where $u_1 = 2$ and $r = \sqrt{3}$ .

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Question Type 1: Finding the nth term given the first term and the common ratio Exercises