Multiple choice

In a sequence, each term follows the pattern Tn = 3Tn - 1 + 2Tn - 2 with T1 = 1, T2 = 2. What is the value of T4?

  1. 17

  2. 19

  3. 26

  4. 28

  5. 35
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D Correct answer
Explanation

Interpreting the recurrence as T_n = 3T_(n-1) + 2T_(n-2), first calculate T_3 = 3(2) + 2(1) = 8. Then T_4 = 3(8) + 2(2) = 28.

AI explanation

Using the given recursive formula Tn = 3Tn-1 + 2Tn-2, we calculate the third term as T3 = 3(2) + 2(1) = 8. Next, the fourth term is T4 = 3(8) + 2(2) = 28.

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