Discussion

Explanation:

For odd n, an + bn = p(n + 1)/2 q(n – 1)/2 + q(n + 1)/2 p(n – 1)/2 = p(n – 1)/2 q(n – 1)/2 (p + q)

Here, p = 1/3, q = 2/3   

∴  p + q = 1

∴  an + bn = p(n – 1)/2 q(n – 1)/2 = (2/9)(n – 1)/2

Now considering options starting from the lowest,

For n = 7, an + bn = 8/729 ≈ 1/91 > 1/100

For n = 9, an + bn = 16/6561 ≈ 1/410 < 1/100

Hence, option (d).

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