Final answer:
To find the 5th term in the sequence defined by an = 4 × 3⁽ⁿ⁻¹⁾, we substitute n with 5 to get a5 = 4 x 3⁴. Calculating 3 to the fourth power gives us 81, which when multiplied by 4 results in 324. Therefore, the 5th term is 324 (option B).
Step-by-step explanation:
The question asks us to use the iterative rule an = 4 × 3⁽ⁿ⁻¹⁾ to find the 5th term in the sequence. To find the 5th term, we substitute n with 5 into the formula:
a⁵ = 4 × 3⁽⁵⁻¹⁾ = 4 × 3⁴
To solve this, we calculate 3 to the power of 4 and multiply the result by 4. Calculating 3⁴, we get 3 × 3 × 3 × 3, which is 81. Multiplying this by 4:
a⁵ = 4 × 81 = 324
Therefore, the 5th term in the sequence is 324, which is option B.