Final answer:
The explicit formula for the geometric sequence 4, 16, 64 is aₙ = 4×4ⁿ⁻¹. To find the explicit formula, determine the common ratio (r) of the sequence and use the formula aₙ = a₁×rⁿ⁻¹. For example, the 5th term of the sequence can be found by substituting n = 5 in the formula.
Step-by-step explanation:
The explicit formula for the geometric sequence 4, 16, 64 is aₙ = 4×4ⁿ⁻¹. (Option a)
To find the explicit formula for a geometric sequence, we need to determine the common ratio (r) of the sequence. In this case, the common ratio is 4 because each term is obtained by multiplying the previous term by 4. Then, we can use the formula aₙ = a₁×rⁿ⁻¹, where a₁ is the first term and r is the common ratio. Substituting the values, we get aₙ = 4×4ⁿ⁻¹.
For example, to find the 5th term of the sequence, we can substitute n = 5 in the formula: a₅ = 4×4⁵⁻¹ = 4×4⁴ = 4×256 = 1024.