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Interleaved squares and cubes: Determine the missing term in 1, 1, 4, 8, 9, 27, 16, ? Odd positions are perfect squares (1², 2², 3², 4², …) and even positions are perfect cubes (1³, 2³, 3³, 4³, …). Compute the 8th term. Choose the correct value.

Q: Interleaved squares and cubes: Determine the missing term in 1, 1, 4, 8, 9, 27, 16, ? Odd positions are perfect squares (1², 2², 3², 4², …) and even positions are perfect cubes (1³, 2³, 3³, 4³, …). Compute the 8th term. Choose the correct value.

Identify the two subsequences Odd indices: 1, 4, 9, 16, … ⇒ 1², 2², 3², 4², … Even indices: 1, 8, 27, … ⇒ 1³, 2³, 3³, … Find the 8th term Position 8 is even ⇒ 4³ = 64.

Difficulty: Easy

Correct Answer: 64

Explanation:

Identify the two subsequences

Odd indices: 1, 4, 9, 16, … ⇒ 1², 2², 3², 4², …
Even indices: 1, 8, 27, … ⇒ 1³, 2³, 3³, …

Find the 8th term
Position 8 is even ⇒ 4³ = 64.

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