1.
a. The sequence is arithmetic because the difference between consecutive terms is constant (8 - 5 = 3, 11 - 8 = 3).
b. 5, 8, 11, __, __, __, __, __, __, __
c. aₙ = 5 + (n - 1) * 3
d. Using the formula aₙ = 5 + (n - 1) * 3 for n = 10:
a₁₀ = 5 + (10 - 1) * 3
a₁₀ = 5 + 9 * 3
a₁₀ = 5 + 27
a₁₀ = 32
e. The patient will walk 32 km during the 10th week.
2.
a. The sequence is geometric because each term is found by multiplying the previous term by a constant factor (2).
b. 1, 2, 4, __, __, __, __, __, __, __
c. aₙ = 1 * 2^(n-1)
d. Using the formula aₙ = 1 * 2^(n-1) for n = 10:
a₁₀ = 1 * 2^(10-1)
a₁₀ = 2^9
a₁₀ = 512
e. There will be 512 viruses in the system after 10 divisions.
Parent Tip: Review the logic above to help your child master the concept of arithmetic and geometric sequence problems.
