The Sequence satisfies the recurrence relation

where k is constant.

If and where a and b are non-zero and

Prove by induction that

for where c is a constant to be found in terms of k, a and b hence find and express and in terms of a,b,c and n

find conditions on a, b and k in the three cases.

i) the sequence is geometric

ii) the sequence has period 2

iii) the sequence has period 4

[OCR STEP(III) 2005, Question 4 ]

I am having some trouble on the induction part of the question, I could do with a tiny bit of guidance, I do not want a full solution just a bit of help if anyone wants to give me a hand.