Question

The question is in the image.

Answer 1

• a) aₙ = 6(n - 1), a₂₄ = 138
• b) aₙ = 2n + 1, a₂₄ = 49

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Sequence a)

Ignoring the hexagon in the middle, we'll count the number of squares:

• 0, 6, 12, ...

This is an AP with the first term of a₁ = 0 and common difference of d = 6.

Explicit formula for an AP is:

• aₙ = a₁ + (n - 1)d

Substitute the first term a₁ and common difference d into equation:

• aₙ = 0 + (n - 1)*6
• aₙ = 6(n - 1)

The 24th term is:

• a₂₄ = 6(24 - 1) = 6(23) = 138

Sequence b)

Count the number of circles:

• 3, 5, 7, ...

This is an AP with the first term of a₁ = 3 and common difference of d = 2.

The explicit formula for this AP is:

• aₙ = 3 + (n - 1)*2
• aₙ = 3 + 2n - 2
• aₙ = 2n + 1

The 24th term is:

• a₂₄ = 2*24 + 1 = 49