Although the number of new wildflowers is decreasing, the total number of flowers is increasing every year (assuming flowers aren't dying or otherwise being removed). Every year, 25% of the number of new flowers from the previous year are added.
The sigma notation would be:
∑ (from n=1 to ∞) 4800 * (1/4)ⁿ , where n is the year.
Remember that this notation should give us the sum of all new flowers from year 1 to infinite, and the values of new flowers for each year should match those given in the table for years 1, 2, and 3
This means the total number of flowers equals:
Year 1: 4800 * 1/4 = 1200 ]
+
Year 2: 4800 * (1/4)² = 300
+
Year 3: 4800 * (1/4)³ = 75
+
Year 4: 4800 * (1/4)⁴ = 18.75 = ~19 (we can't have a part of a flower)
+
Year 5: 4800 * (1/4)⁵ = 4.68 = ~ 5
+
Year 6: 4800 * (1/4)⁶ = 1.17 = ~1
And so on. As you can see, it in the years that follow the number of flowers added approaches zero. Thus, we can approximate the infinite sum of new flowers using just Years 1-6:
1200 + 300 + 75 + 19 + 5 + 1 = 1,600
192 = total beads
necklace + bracelet = 192
Let x equal the number of beads
bracelet = 5x
necklace = x
5x + x = 192
6x = 192
x = 32
It takes 32 beads to make a necklace
Your rise over run will be -3 over 1 your going to start at the point 5 on the y-axis when your at the point 5 go down 3 then over to the right 1 keep going till it off the graph. Now do the opposite way and go up 3 from 5 and to the left 1 and keep doing that till it’s off the graph.
Hope this helps
Commutative property of addition
