Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes. Show that the number of hydrogen atoms (represented by an H ) in the three alkanes pictured forms an arithmetic sequence.

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes. From the above diagram, The number of hydrogen atoms in a chemical structure of methane = 4 The number of hydrogen atoms in a chemical structure of ethane = 6 The number of hydrogen atoms in a chemical structure of propane = 8 So, the sequence can be formed as 4 , 6 , 8 Thus, clearly, first term = 4 and common difference = 6 - 4 = 8 - 6 = 2 Hence, clearly, the sequence forms as arithmetic sequence as the difference between any consecutive terms is a constant.

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes. Let u n be the number of hydrogen atoms in an alkane with n carbon C atoms. Write down an explicit formula for u n .

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes. From the above diagram, The number of hydrogen atoms in a chemical structure of methane = 4 The number of hydrogen atoms in a chemical structure of ethane = 6 The number of hydrogen atoms in a chemical structure of propane = 8 So, the sequence can be formed as 4 , 6 , 8 Thus, clearly, first term, u 1 = 4 and common difference , d = 6 - 4 = 8 - 6 = 2 Hence, clearly, the sequence forms as arithmetic sequence as the difference between any consecutive terms is a constant. Let u n be the number of hydrogen atoms in an alkane with n carbon C atoms. Now, the explicit formula for u n is u n = u 1 + ( n - 1 ) d , where u 1 is the first term.

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes. Let u n be the number of hydrogen atoms in an alkane with n carbon C atoms. Find the number of hydrogen atoms in an alkane with 20 carbon atoms.

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes. From the above diagram, The number of hydrogen atoms in a chemical structure of methane = 4 The number of hydrogen atoms in a chemical structure of ethane = 6 The number of hydrogen atoms in a chemical structure of propane = 8 So, the sequence can be formed as 4 , 6 , 8 Thus, clearly, first term, u 1 = 4 and common difference, d = 6 - 4 = 8 - 6 = 2 Hence, clearly, the sequence forms as arithmetic sequence as the difference between any consecutive terms is a constant. Let u n be the number of hydrogen atoms in an alkane with n carbon C atoms. So, according to the question, we have n = 20 Therefore, the number of hydrogen atoms in an alkane is u n = 4 + ( 20 - 1 ) 2 = 4 + 38 = 42 .

EASY

MYP:4-5

IMPORTANT

Earn 100

A geometric sequence has common ratio $4$ and the $2^{n d}$ term is $9$ more than the $1^{s t}$ term. Write down two different expressions for the second term in terms of $u_{1}$ , the $1^{s t}$ term.

Important Questions on Arithmetic and Geometric Sequences

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Mixed practice>Q 8

A geometric sequence has common ratio

4

and the

2^{n d}

term is

9

more than the

1^{s t}

term. Write an equation in

u_{1}

and find the value of

u_{1}

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Mixed practice>Q 8

A geometric sequence has common ratio

4

and the

2^{n d}

term is

9

more than the

1^{s t}

term. Find the number of terms in the sequence that are less than

1000

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Mixed practice>Q 9

A geometric sequence has first term

12

and the third term

48

. The common ratio is

r

. Show that

r^{2} = 4

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Mixed practice>Q 9

A geometric sequence has first term

12

and the third term

48

. The common ratio is

r

. Find the possible values for the common ratio.

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Mixed practice>Q 9

A geometric sequence has first term

12

and the third term

48

. The common ratio is

r

. Find the possible values of the

6^{t h}

term.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Review in context>Q 1

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes.

Question Image

Show that the number of hydrogen atoms (represented by an $H$ ) in the three alkanes pictured forms an arithmetic sequence.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Review in context>Q 1

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes.

Question Image

Let $u_{n}$ be the number of hydrogen atoms in an alkane with $n$ carbon $(C)$ atoms. Write down an explicit formula for $u_{n}$ .

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 10 - Arithmetic and Geometric Sequences>Review in context>Q 1

Consider the following diagram, which illustrates the chemical structure of methane, ethane and propane, three examples of chemicals known as alkanes.

Question Image

Let $u_{n}$ be the number of hydrogen atoms in an alkane with $n$ carbon $(C)$ atoms.

Find the number of hydrogen atoms in an alkane with $20$ carbon atoms.

A geometric sequence has common ratio 4 and the 2nd term is 9 more than the 1st term. Write down two different expressions for the second term in terms of u1, the 1st term.

Important Questions on Arithmetic and Geometric Sequences

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A geometric sequence has common ratio $4$ and the $2^{n d}$ term is $9$ more than the $1^{s t}$ term. Write down two different expressions for the second term in terms of $u_{1}$ , the $1^{s t}$ term.