Geometric series

1.

First term  =  510

Common ratio  = 1.12

Recursive Rule     a_n  =  a_n-1 * (1.12),   a₁  = 510

2.   Explicit Rule

a_n  = 510 * (1.12)^(n - 1)

3. Phones sold in week 3

a₃  = 510 * (1.12)^(3 - 1)  =  510 * (1.12)^2  ≈ 640 phones

4. Phones sold in first year  =

510 * [ 1 - 1.12^52] / [ 1 - 1.12]  ≈  1,536,478   phones