Question

!WARNING! !CONFUSING! !WARNING! please help

12 flowers were planted in a row, and after that between each two flowers was planted one more flower. Then, the same pattern was repeated four more times. In total, how many flowers have been planted ?

Answer 1

Starting with 12 flowers and repeatedly adding a flower between each pair, the total number of flowers after five iterations is 353 flowers.

Step-by-step explanation:

Initially, 12 flowers were planted in a row. After planting one more between each of the two flowers, the number increases because we add another 11 flowers. Now we have a total of 23 flowers. When the same pattern is repeated four more times, we should consider the pattern that adds an additional flower between each existing pair. After the first repeat, we have (23 - 1) + 23 = 45 flowers. Each subsequent repeat doubles the previous number of gaps and adds that many flowers. Here is the progression:

1. First planting: 12 flowers
2. After first addition: 12 + (12 - 1) = 23 flowers
3. Second addition: 23 + (23 - 1) = 45 flowers
4. Third addition: 45 + (45 - 1) = 89 flowers
5. Fourth addition: 89 + (89 - 1) = 177 flowers
6. Fifth addition: 177 + (177 - 1) = 353 flowers

The total number of flowers planted after repeating the pattern five times (the initial planting plus four additional iterations) is 353 flowers.