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Answer:

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Step-by-step explanation:

Given the recursive formula [tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex] and

[tex]a_{4}[/tex] = 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{9}{4}[/tex], then

[tex]\frac{a_{3} }{4}[/tex] = [tex]\frac{9}{4}[/tex] ( multiply both sides by 4 )

a₃ = 4 × [tex]\frac{9}{4}[/tex] = 9

[tex]\frac{a_{2} }{4}[/tex] = 9 ( multiply both sides by 4 )

a₂ = 36

[tex]\frac{a_{1} }{4}[/tex] = 36 ( multiply both sides by 4 )

a₁ = 144

The first 4 terms are

144, 36, 9, 2 [tex]\frac{1}{4}[/tex]

The first four terms of the recursive formula are 144, 36, 9, 9/4 .

What is a recursive sequence ?

A recursive sequence is an infinite sequence of numbers where each number in the sequence is equal to a fixed linear combination of one or more of its before or after number. In a recursive sequence, the series of the number present follows a particular sequence of logic.

How to solve the given recursive sequence ?

Given series is an = (an-1)/4 and also a4 = 9/4

Putting n = 4 in the given recursive sequence,

⇒ a3/4 = a4

∴  a3 = a4 * 4 = 9/4 * 4 = 9

Again putting n = 3 in the given recursive sequence,

⇒ a2 = 4*a3

∴  a2 = 4 * 9 = 36

Finally putting n = 2 in the recursive sequence,

⇒ a1 = 4 * a2

∴  a1 = 4 * 36 = 144

Therefore, the first four terms of the recursive formula are 144, 36, 9, 9/4 .

To learn more about recursive formula, refer -

https://brainly.com/question/1275192

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