Question

Write the first five terms of the recursively defined sequence. a1 = 6, ak 1 = 1 3 ak2

Answer 1

The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

For given question,

We have been given the recursive formula of a sequence.

$a_{k+1}=\frac{1}{3}{a_k}^2$

Also, the first term of the sequence is,

a1 = 6

Substitute k = 1 in given recursive formula.

⇒ $a_{1+1}=\frac{1}{3}{a_1}^2$

⇒ a2 = 1/3 (6)²

⇒ a2 = (1/3) × 36

⇒ a2 = 12

Substitute k = 2 in given recursive formula.

⇒ $a_{2+1}=\frac{1}{3}{a_2}^2$

⇒ a3 = (1/3) × (12)²

⇒ a3 = (1/3) × 144

⇒ a3 = 48

Substitute k = 3 in given recursive formula.

⇒ $a_{3+1}=\frac{1}{3}{a_3}^2$

⇒ a4 = (1/3) × (48)²

⇒ a4 = (1/3) × 2304

⇒ a4 = 768

Substitute k = 4 in given recursive formula.

⇒ $a_{4+1}=\frac{1}{3}{a_4}^2$

⇒ a5 = (1/3) × (768)²

⇒ a5 = (1/3) × 589824

⇒ a5 = 196608

Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

Learn more about the recursive formula of sequence here:

brainly.com/question/14457800

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