Give a recursive definition of the sequence {a_n}, n = 1,2,3,...if a sub n = n(n + 1).

Solution:

Given {a_n}, n = 1,2,3,...if a sub n = n(n + 1).

When n = 1 ⇒ a₁ = 1(1 + 1) = 1(2) = 2

When n = 2 ⇒ a₂ = 2(2 + 1) = 2(3) = 6

When n = 3 ⇒ a₃ = 3(3 + 1) = 3(4) = 12

When n = 4 ⇒ a₄ = 4(4 + 1) = 4(5) = 20

When n = 5 ⇒ a₅ = 5(5 + 1) = 5(6) = 30

When n = 6 ⇒ a₆ = 6(6 + 1) = 6(7) = 42

Hence, the recursive definition of the given sequence is 2, 6, 12, 20, 30, 42…

Give a recursive definition of the sequence {a_n}, n = 1, 2, 3,... if a sub n = n(n + 1).

Summary:

A recursive definition of the sequence {a_n}, n = 1, 2, 3,... if a sub n = n(n + 1) is given as 2, 6, 12, 20, 30, 42…