Given a_0 = 4 and a_n = 3 a_{n-1} − 2. What is a_4?

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Multiple Choice

Given a_0 = 4 and a_n = 3 a_{n-1} − 2. What is a_4?

Explanation:
This recurrence builds each term by tripling the previous one and subtracting 2, so go step by step from a_0. a_1 = 3·a_0 − 2 = 3·4 − 2 = 12 − 2 = 10 a_2 = 3·a_1 − 2 = 3·10 − 2 = 30 − 2 = 28 a_3 = 3·a_2 − 2 = 3·28 − 2 = 84 − 2 = 82 a_4 = 3·a_3 − 2 = 3·82 − 2 = 246 − 2 = 244 So a_4 = 244.

This recurrence builds each term by tripling the previous one and subtracting 2, so go step by step from a_0.

a_1 = 3·a_0 − 2 = 3·4 − 2 = 12 − 2 = 10

a_2 = 3·a_1 − 2 = 3·10 − 2 = 30 − 2 = 28

a_3 = 3·a_2 − 2 = 3·28 − 2 = 84 − 2 = 82

a_4 = 3·a_3 − 2 = 3·82 − 2 = 246 − 2 = 244

So a_4 = 244.

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