Question

Find a₈ and a₁₅ whose n^th term is a_n = `{{:(("n"^2 - 1)/("n" + 3)";", "n is even"","  "n ∈ N"),(("n"^2)/(2"n" + 1)";", "n is odd"","  "n ∈ N"):}`

Answer 1

a_n = `{{:(("n"^2 - 1)/("n" + 3)";", "n is even"),(("n"^2)/(2"n" + 1)";", "n is odd"):}`

a₈ = `("n"^2 - 1)/("n" + 3) = (8^2 - 1)/(8 + 3) = (64 - 1)/11 = 63/11`

a₁₅ = `"n"^2/(2"n" + 1) = 15^2/(2 xx 15 + 1) = 225/(30 + 1) = 225/31`