Calculating Flowers and Patterns

In a magical garden, there are several plants that produce a specific number of flowers each week. The number of flowers produced by the plants according to the following rule:

If a plant produces x flowers in week 1, then in week 2 it produces 2x + 1 flowers, in week 3 it produces 3x + 3 flowers, and so on. After 5 weeks, the total number of flowers produced by a plant is 105. What was the number of flowers produced by the plant in week 1?

Let x be the number of flowers produced in week 1. The total number of flowers produced after 5 weeks can be expressed as:

$$ x + (2x + 1) + (3x + 3) + (4x + 6) + (5x + 10) = 105 $$