A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula?–12, –18, –27, ...–20, 30, –45, ...–18, –16.5, –15, ...–16, –17.5, –19, ...
Accepted Solution
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Answer:The sequence -12 , -18 , -27 , ............ is generated using the formula ⇒ 1st sequenceStep-by-step explanation:The recursive formula of the sequence is f(n + 1) = 1.5 f(n)That means there is a constant ratio 1.5 between each two consecutive termsIn sequence -12 , -18 , -27 , ............The first term is -12The formula is f(n + 1) = 1.5 f(n)Use the first term where n = 1 to find the 2nd term∵ f(1) = -12- Substitute n by 1 in the given formula∵ f(1 + 1) = 1.5 f(1)∴ f(2) = 1.5(-12)∴ f(2) = -18Use the second term where n = 2 to find the 3rd term∵ f(2) = -18- Substitute n by 2 in the given formula ∵ f(2 + 1) = 1.5 f(2)∴ f(3) = 1.5(-18)∴ f(3) = -27∴ The sequence -12 , -18 , -27 , ............ is generated using the formula