Question

Select the correct answer from each drop-down menu.

Answer 1

Answer:

$d_{n+1}=d_n\,+\,2^n$

with $d_1=81$

Step-by-step explanation:

We can study what happens day by day starting with day one (1) to understand how the recursive relation can be constructed:

Day #     Number of stamps     What is added relative to previous day

1               d1 = 80 + 1 = 81

2              d2 = 81 + 2 = 83            d2 = d1 + 2

3              d3 = 83 + 4 = 87           d3 = d2 + $2^2$

4              d4 = 87 + 8 = 95           d4 = d3 + $2^3$

5              d5 = 95 + 16 = 111          d5 = d4 + $2^4$

6              d6 = 111 + 32 = 143        d6 = d5 + $2^2$

(n+1)                                               d(n+1) = dn + $2^n$