Question

Give a recursive definition of the following sequences, in other words, give a formula for aₙ+1 in terms of aₙ (and also specify the initial value a₁ ):

a) aₙ=7 n b

Answer 1

The recursive definition for the sequence aₙ=7ⁿ is aₙ+₁ = 7aₙ, with an initial value of 7 for a₁.

Step-by-step explanation:

To give a recursive definition of the sequence aₙ=7ⁿ, we can express the next term aₙ+₁ in terms of the current term aₙ. In this case, aₙ+₁ can be calculated by multiplying aₙ by 7. So the recursive definition is: aₙ+₁ = 7aₙ. The initial value a₁ is 7, since a₁ is the first term of the sequence.