Give a recursive definition of sequence a_n = 2ⁿ, n = 2, 3, 4... where a₁ = 2.

Solution:

Given a_n = 2ⁿ, n = 2, 3, 4... where a₁ = 2.

When n = 2 ⇒ a₂ = 2² = 4 ⇒ a₂ = 4

When n = 3 ⇒ a₃ = 2³ = 8 ⇒ a₃ = 8

When n = 4 ⇒ a₄ = 2⁴ =16 ⇒ a₄= 16

When n = 5 ⇒ a₅ = 2⁵ = 32 ⇒ a₅ = 32

When n = 6 ⇒ a₆ = 2⁶ = 64 ⇒ a₆ = 64

Hence, the recursive definition of the given sequence is 2, 4, 8, 16, 32, 64…..

Give a recursive definition of sequence a_n = 2ⁿ, n = 2, 3, 4... where a₁ = 2.

Summary:

A recursive definition of sequence a_n = 2ⁿ, n = 2, 3, 4... where a₁ = 2 is given as 2, 4, 8, 16, 32, 64...