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d. 40; 200; 1000; 5000 e. 6; 36; 216; 1296 f. 3; 9; 27; 81; 243 g. 5; 20; 80; 320; 1280 h. 7; 42; 252; 1512 i. 9; 45; 225; 1125 j. 10; 20; 40; 80; 160

Mathematics

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Answers

6 parts
d

25000\text{25000}

e

7776\text{7776}

f

729\text{729}

g

5120\text{5120}

h

9072\text{9072}

h(i)

5625\text{5625}

320\text{320}

Step-by-step solution

14 steps

Here are the next terms for each sequence:

Part d· 2 steps

  1. Find the common ratio.

    408=5\frac{40}{8} = 5 20040=5\frac{200}{40} = 5

    The common ratio is 5.

  2. Multiply the last term by the common ratio.

    5000×5=250005000 \times 5 = 25000

    The next term is 25000\boxed{\text{25000}}.

Part e

7776\text{7776}

  1. Find the common ratio.

    61=6\frac{6}{1} = 6 366=6\frac{36}{6} = 6

    The common ratio is 6.

  2. Multiply the last term by the common ratio.

    1296×6=77761296 \times 6 = 7776

    The next term is 7776\boxed{\text{7776}}.

Part f

729\text{729}

  1. Find the common ratio.

    93=3\frac{9}{3} = 3 279=3\frac{27}{9} = 3

    The common ratio is 3.

  2. Multiply the last term by the common ratio.

    243×3=729243 \times 3 = 729

    The next term is 729\boxed{\text{729}}.

Part g

5120\text{5120}

  1. Find the common ratio.

    205=4\frac{20}{5} = 4 8020=4\frac{80}{20} = 4

    The common ratio is 4.

  2. Multiply the last term by the common ratio.

    1280×4=51201280 \times 4 = 5120

    The next term is 5120\boxed{\text{5120}}.

Part h

9072\text{9072}

  1. Find the common ratio.

    427=6\frac{42}{7} = 6 25242=6\frac{252}{42} = 6

    The common ratio is 6.

  2. Multiply the last term by the common ratio.

    1512×6=90721512 \times 6 = 9072

    The next term is 9072\boxed{\text{9072}}.

Part h(i)

5625\text{5625}

  1. Find the common ratio.

    459=5\frac{45}{9} = 5 22545=5\frac{225}{45} = 5

    The common ratio is 5.

  2. Multiply the last term by the common ratio.

    1125×5=56251125 \times 5 = 5625

    The next term is 5625\boxed{\text{5625}}.

    j)

  3. Find the common ratio.

    2010=2\frac{20}{10} = 2 4020=2\frac{40}{20} = 2

    The common ratio is 2.

  4. Multiply the last term by the common ratio.

    160×2=320160 \times 2 = 320

    The next term is 320\boxed{\text{320}}.

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