A skier has decided that on each trip down a slope, she will do 2 more jumps than before. On her first trip she did 6 jumps. Derive the sigma notation that shows how many total jumps she attempts from her fourth trip down the hill through her twelfth trip. Then solve for how many total jumps she attempts from her second trip down the hill through her tenth trip.

the summation of 2 i plus 4 from i equals 2 to 10. ; 144 jumps

the summation of 2 i plus 4 from i equals 2 to 10. ; 180 jumps

the summation of 4 i plus 2 from i equals 2 to 10. ; 234 jumps

the summation of 4 i plus 2 from i equals 2 to 10. ; 306 jumps

I Have NO IDEA OMFG

Me neither

Its so obvious, 10. ; 144 jumps

the summation of 2 i plus 4 from i equals 2 to 10. ; 180 jumps

To derive the sigma notation that shows the total number of jumps from the fourth trip through the twelfth trip, we need to determine the terms of the series.

Let's analyze the problem step by step.

First, we know that on the first trip, the skier did 6 jumps. We are interested in finding the total number of jumps from the fourth trip through the twelfth trip. Let's find the number of jumps made on each trip:

1st trip: 6 jumps
2nd trip: 6 + 2 = 8 jumps (2 more than the previous trip)
3rd trip: 8 + 2 = 10 jumps
4th trip: 10 + 2 = 12 jumps
5th trip: 12 + 2 = 14 jumps
...
12th trip: 22 + 2 = 24 jumps

To represent the series using sigma notation, we can use the variable i as the index for each term. The expression 2i + 4 represents the number of jumps on each trip.

The sigma notation for the total number of jumps from the fourth trip through the twelfth trip is:

Σ (2i + 4) for i = 4 to 12

Now, let's solve for the total number of jumps from the second trip through the tenth trip.

Again, we need to determine the terms of the series.

2nd trip: 6 + 2 = 8 jumps
3rd trip: 8 + 2 = 10 jumps
4th trip: 10 + 2 = 12 jumps
...
10th trip: 18 + 2 = 20 jumps

The sigma notation for the total number of jumps from the second trip through the tenth trip is:

Σ (2i + 4) for i = 2 to 10

Finally, let's calculate the results for the two sigma notations:

The summation of (2i + 4) for i = 4 to 12 is equal to 144 jumps.
The summation of (2i + 4) for i = 2 to 10 is equal to 180 jumps.