Question: 1.Show that a n = 2 n 5 n is also a solution to the recurrence relation a n = 7a n1 10a n2. What

1.Show that a_n= 2ⁿ 5ⁿis also a solution to the recurrence relation a_n= 7a_n1 10a _n2.What would the initial conditions need to be for this to be the closed formula for the sequence?

2. Consider the sum 4 + 11 + 18 + 25 + + 249.

(a) How many terms (summands) are in the sum?

(b) Compute the sum using a technique discussed in this section

3.Suppose a_n = n² + 3n + 4.Find a closed formula for the sequence of differences by computing a_n a_n 1

4.Solve the recurrence relation a_n= 3a_n1+ 10a_n2with initial terms a₀= 4 and a₁ = 1

5.Prove, by mathematical induction, that F₀ + F₁+ F₂+ + F_nF_n+21, where F_nis the nth Fibonacci number (F₀=0, F_{1 =}1 and F_n= F_n1 + F_n2)

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