A geometric sequence begins 6 , 3 , 1 . 5 , … Write down an explicit formula for the nth term.

Given geometric sequence is 6 , 3 , 1 . 5 , … To find: An explicit formula for the nth term. Since the given sequence is a geometric sequence And, a geometric sequence is one in which any term divided by the previous term is a constant. This constant is called the common ratio of the sequence. Let the nth term of the given geometric sequence be denoted by u n . Then, u 1 = 6 , u 2 = 3 Thus, according to the definition of the common ratio r , we have r = u 2 u 1 = 3 6 = 1 2 And, u 1 = First term of the sequence. Hence, first term of the sequence = 6 , and common ratio = 1 2 . Now, we know that a geometric sequence with first term a and common ratio r has a explicit formula, u n = a r n - 1 Thus, the explicit formula for the nth term of the given geometric sequence is u n = 6 1 2 n - 1 .

E M B I B E

MYP Mathematics A concept based approach 4&5 Standard>Generalization>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice

Rose Harrison and Clara Huizink Solutions for Exercise 17: Mixed practice

Author:Rose Harrison & Clara Huizink

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison and Clara Huizink Solutions for Exercise 17: Mixed practice

Attempt the practice questions from Exercise 17: Mixed practice with hints and solutions to strengthen your understanding. MYP Mathematics A concept based approach 4&5 Standard solutions are prepared by Experienced Embibe Experts.

Questions from Rose Harrison and Clara Huizink Solutions for Exercise 17: Mixed practice with Hints & Solutions

MEDIUM

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice>Q 7

A geometric sequence begins $6, 3, 1.5, \dots$ Write down an explicit formula for the $nth$ term.

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MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice>Q 7

A geometric sequence begins $6, 3, 1.5, \dots$ Find the value of the tenth term, correct to three significant figures.

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice>Q 8

A geometric sequence has common ratio $4$ . The second term is $9$ more than the first term. Write down two different expressions for the second term in terms of $a$ .

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MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice>Q 8

A geometric sequence has common ratio $4$ . The second term is $9$ more than the first term. Find the value of the first term.

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MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice>Q 8

A geometric sequence has common ratio $4$ . The second term is $9$ more than the first term. Find how many terms there are in the sequence that are less than $1000$ .

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice>Q 9

A geometric sequence has first term $12$ and third term $48$ . The common ratio is $r$ . Show that $r^{2} = 4$ .

EASY

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 26 - Growing Predictably (Arithmetic and Geometric Sequences)>Mixed practice>Q 9

A geometric sequence has first term $12$ and third term $48$ . The common ratio is $r$ . Hence, find two possible values for the common ratio.

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MYP:4-5