Grade 9 Algebraic Expressions Patterns

Questions on identifying patterns of a algebraic expressions are presented along with their solutions.

Questions

Question 1: Identify the pattern and write the next term:

1, x^{2}, x^{4}, x^{6}, x^{8}, - - -

.
Question 2: Extend the pattern and write the next term:

x^{10}, x^{8}, x^{6}, x^{4}, x^{2}, - - -

.
Question 3: Extend the pattern:

x + y, 2 x + y, 3 x + y, 4 x + y, - - -

.
Question 4: Identify the pattern and write the next term:

2 x, 4 x + 1, 6 x + 2, 8 x + 3, - - -

.
Question 5: Identify the pattern and find the next term:

x + y + 1, 2 x + 3 y + 1, 3 x + 5 y + 1, 4 x + 7 y + 1, - - -

.
Question 6: Identify the pattern and write the next term:

x^{3} + 10 x, x^{3} + 9 x, x^{3} + 8 x, x^{3} + 7 x, - - -

.
Question 7: Extend the pattern and write the next term:

3 a + 2, 6 a + 5, 12 a + 11, 24 a + 23, - - -

.
Question 8: Identify the pattern and write the next term::

1, 2 x^{2}, 4 x^{4}, 8 x^{6}, 16 x^{8}, - - -

.
Question 9: Extend the pattern and write the next term::

x + y, x^{2} y + y^{2} x, x^{3} y^{2} + y^{3} x^{2}, x^{4} y^{3} + y^{4} x^{3}, - - -

.
Question 10: Extend the pattern and write the next term::

x^{10} y^{10}, x^{11} y^{9}, x^{12} y^{8}, x^{13} y^{7}, - - -

Solutions

Solution to Question 1: The pattern is obtained by multiplying terms by

x^{2}

to obtain the next term.

1

: first term

1 \times x^{2} = x^{2}

x^{2} \times x^{2} = x^{2 + 2} = x^{4}

x^{4} \times x^{2} = x^{4 + 2} = x^{6}

x^{6} \times x^{2} = x^{6 + 2} = x^{8}

Next term is:

x^{8} \times x^{2} = x^{8 + 2} = x^{10}

Solution to Question 2: The pattern is obtained by dividing by

x^{2}

to obtain the next term.

x^{10}

: first term

\frac{x^{10}}{x^{2}} = x^{10 - 2} = x^{8}

\frac{x^{8}}{x^{2}} = x^{8 - 2} = x^{6}

\frac{x^{6}}{x^{2}} = x^{6 - 2} = x^{4}

\frac{x^{4}}{x^{2}} = x^{4 - 2} = x^{2}

Next term is:

\frac{x^{2}}{x^{2}} = 1

Solution to Question 3: The pattern is obtained by adding

x

to obtain the next term.

x + y

: first term

x + y + x = 2 x + y

2 x + y + x = 3 x + y

3 x + y + x = 4 x + y

Next terms is

4 x + y + x = 5 x + y

.
Solution to Question 4: The pattern is obtained by adding

2 x + 1

to obtain the next term.

2 x

: first term

2 x + 2 x + 1 = 4 x + 1

4 x + 1 + 2 x + 1 = 6 x + 2

6 x + 2 + 2 x + 1 = 8 x + 3

Next terms is

8 x + 3 + 2 x + 1 = 10 x + 4

.
Solution to Question 5: The pattern is obtained by adding

x + 2 y

to obtain the next term.

x + y + 1

: first term

x + y + 1 + x + 2 y = 2 x + 3 y + 1

2 x + 3 y + 1 + x + 2 y = 3 x + 5 y + 1

3 x + 5 y + 1 + x + 2 y = 4 x + 7 y + 1

Next terms is

4 x + 7 y + 1 + x + 2 y = 5 x + 9 y + 1

.
Solution to Question 6: The pattern is obtained by subtracting

x

to obtain the next term.

x^{3} + 10 x

: first term

x^{3} + 10 x - x = x^{3} + 9 x

x^{3} + 9 x - x = x^{3} + 8 x

x^{3} + 8 x - x = x^{3} + 7 x

Next term is

x^{3} + 7 x - x = x^{3} + 6 x

.
Solution to Question 7: The pattern is obtained by doubling and adding

1

to obtain the next term.

3 a + 2

: first term

2 (3 a + 2) + 1 = 6 a + 4 + 1 = 6 a + 5

2 (6 a + 5) + 1 = 12 a + 10 + 1 = 12 a + 11

2 (12 a + 11) + 1 = 24 a + 22 + 1 = 24 a + 23

Next term is

2 (24 a + 23) + 1 = 48 a + 46 + 1 = 48 a + 47

Solution to Question 8: The pattern is obtained by mutliplying by

2 x^{2}

to obtain the next term.

1

: first term

1 \times 2 x^{2} = 2 x^{2}

2 x^{2} \times 2 x^{2} = 4 x^{2 + 2} = 4 x^{4}

4 x^{4} \times 2 x^{2} = 8 x^{4 + 2} = 8 x^{6}

8 x^{6} \times 2 x^{2} = 16 x^{6 + 2} = 16 x^{8}

Next term is

16 x^{8} \times 2 x^{2} = 32 x^{8 + 2} = 32 x^{10}

Solution to Question 9: The pattern is obtained by mutliplying by

x y

to obtain the next term.

x + y

: first term

(x + y) x y = x^{2} y + y^{2} x

(x^{2} y + y^{2} x) x y = x^{3} y^{2} + y^{3} x^{2}

(x^{3} y^{2} + y^{3} x^{2}) x y = x^{4} y^{3} + y^{4} x^{3}

Next terms is

(x^{4} y^{3} + y^{4} x^{3}) x y = x^{5} y^{4} + y^{5} x^{4}

.
Solution to Question 10: The pattern is obtained by mutliplying by

\frac{x}{y}

to obtain the next term.

x^{10} y^{10}

: first term

x^{10} y^{10} \times \frac{x}{y} = x^{10 + 1} y^{10 - 1} = x^{11} y^{9}

x^{11} y^{9} \times \frac{x}{y} = x^{11 + 1} y^{9 - 1} = x^{12} y^{8}

x^{12} y^{8} \times \frac{x}{y} = x^{12 + 1} y^{8 - 1} = x^{13} y^{7}

Next terms is

x^{13} y^{7} \times \frac{x}{y} = x^{13 + 1} y^{7 - 1} = x^{14} y^{6}

Grade 9 Algebraic Expressions Patterns

Questions

Solutions

More References and Links