This is question 4 on June 2008 Further Pure 1 paper OCR (downloadable for OCR website) OCR > Qualifications > By type > AS/A Level GCE (current) > Mathematics > Mathematics > All documents

The question goes:

The MatrixAis given byA=

3, 1,

0, 1,

prove by induction that for n>1

A^n =

3^n, 0.5(3^n -1),

0, 1,

I just dont get how 3^k + 0.5(3^k -1) becomes 0.5(3^k+1 -1)

Thanks