Hint for Section 8.3 Question 2

2. Consider the recurrence relation  a_k = 2 a_k-1 + 15 a_k-2   for all integers k2. To find all the sequences of the form 1, t, t², t³, ..., tⁿ,... which satisfy this recurrence relation you need to solve the characteristic equation of the relation.

Recall that for a second-order linear homogeneous recurrence relation with constant coefficients: a_k = A · a_k-1 + B · a_k-2    for all integers k 2, the characteristic equation of the relation is t² - A · t - B = 0.

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