Logic - Proof by Induction - Need help

[amirsad]

Hi can someone help me answer this question I'm stuck on.

(b) A sequence of integers x₁, x₂, ..., x_k,..., is defined recursively as follows: x₁ = 2 and x_k+1 = 7x_k for k > 1.

(i) Calculate x₂, x₃, and x₄.
(ii) Deduce a formula for the n-th term -- that is, x_n in terms of n -- and then prove its validity, using the principle of mathematical induction.

Also can you show me how you do it. Thanks

 

[stapel]

(b) A sequence of integers x₁, x₂, ..., x_k,..., is defined recursively as follows: x₁ = 2 and x_k+1 = 7x_k for k > 1.

(i) Calculate x₂, x₃, and x₄.
(ii) Deduce a formula for the n-th term -- that is, x_n in terms of n -- and then prove its validity, using the principle of mathematical induction.

Also can you show me how you do it. Thanks

I've typed out the exercise for you. Now you can do part (i), which is a simple matter of multiplication.

For part (ii), first study this lesson on how to do induction proofs. Once you have completed that lesson (including working through all of the examples for yourself), please attempt part (ii). If you get stuck, you can then reply with a clear listing of your efforts so far. Thank you!