Solution for Section 8.1 Question 4

4. Given the sequence 5, 10, 20, 40, ... , 5 · 2^k, ... for  k0,  we can find explicit formulae for the nth term, a_n,  and the (n-1)th term, a_n-1.

a_n = 5 · 2ⁿ     and    a_n-1 = 5 · 2^n-1.

Hence 2 · a_n-1 = 2 · 5 · 2^n-1 = 5 · 2ⁿ = a_n.    Thus this sequence satisfies the recurrence relation  a_n = 2 · a_n-1  for all integers n1.

Back to Section 8.1