16. Use the formulas F_n+4 = 3F_n+1 + 2F_n and F_n+1 = F_n+2 - F_n to express F_n+4 in terms of F_n+2 and F_n.

17. Show the following:

(a) 2(F₀ + F₃ + F₆ + F₉ + F₁₂) = F₁₄ - 1.

(b) 2(F₀ + F₃ + F₆ + F₉ + F₁₂ + F₁₅) = F₁₇ - 1.

18. Show the following:

(a) 2(F₁ + F₄ + F₇ + F₁₀ + F₁₃) = F₁₅.

(b) 2(F₁ + F₄ + F₇ + F₁₀ + F₁₃ + F₁₆) = F₁₈.

19. By addition of corresponding sides of formulas of the two previous problems, find expressions for:

(a) 2(F₂ + F₅ + F₈ + F₁₁ + F₁₄).

(b) 2(F₂ + F₅ + F₈ + F₁₁ + F₁₄ + F₁₇).

20.   (i) Prove that F_n+3 - 4F_n - F_n-3 = 0 for n3.
       (ii) Prove that F_n+4 - 7F_n + F_n-4 = 0 for n4.
    *(iii) For m4, find a compact expression for F_a + F_a+4 + F_a+8 + ... + F_a+4m.

21. Evaluate each of the following sums:

(a)

(b) 

(c) 

(d) 

(e) 
 

(f) 

22. Find m, given that
 

Wednesday, May 24, 2000