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Write the next two apparent terms of the sequence. Describe the pattern you used to find these terms. 5, 10, 20, 40

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Answer:

80, 160

Explanation:

this is a geometric sequence

formula = ar^(n-1)

where a is the first term and r is the ratio/multiple

r = 10/5 = 20/10 = 40/20 = 2

we know first term is 5. put this into formula

ar^(n-1) = (5)(2)^(n-1) = 5(2)^(1-1) = 5(2)^0 = 5(1) = 5.

second term is 10

confirm this with formula.

ar^(n-1) = 5(2)^(2-1) = 5(2)^1 = 5(2) = 10

so to find next two terms (the fifth and sixth terms):

ar^(n-1) = (5)(2)^(5-1) = (5)(2)^(4) = 5(16) = 80. this is fifth term

ar^(n-1) = (5)(2)^(6-1) = (5)(2)^(5) = 5(32) = 160. this is sixth term

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