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Yuri [45]
4 years ago
12

Find the first four terms of the recursive sequence defined by the following formula:

Mathematics
2 answers:
tatuchka [14]4 years ago
8 0

Answer:

144, 36, 9, 21/4

Step-by-step explanation:

NISA [10]4 years ago
4 0

Answer:

144, 36, 9, 2 \frac{1}{4}

Step-by-step explanation:

The recursive formula allows us to find a term in a sequence from the previous term.

Given

a_{n} = \frac{a_{n-1} }{4}

Given the fourth term we require to work back to the third term , second and so on. Rearrange the formula to give

Multiply both sides by 4, then

a_{n-1} = 4a_{n}

Given a₄ = 2 \frac{1}{4}, then

a₃ = 4 × a₄ = 4 × 2\frac{1}{4} = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

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