Question

A skier has decided that on each trip down a slope, she will do 3 more jumps than before. On her first trip she did 5 jumps. Derive the sigma notation that shows how many total jumps she attempts from her third trip down the hill through her tenth trip. Then solve for the number of total jumps from her third to tenth trips.

Answer 1

Alright. Trip 1 was 5 jumps. Let's set up sigma here. It is from the third jump, so the lower index is n=3, to the tenth, so the upper index is 10.
So far we have this:
\[\sum_{n=3}^{10}\]
For the numerical portion: the format is a1+d(n-1)
a1 is 5
d is 3
5+3(n-1)
Simplify it
5+3n-3
2+3n

We have set up Sigma notation.
\[\sum_{n=3}^{10}2+3n\]

Now to solve this.
first solve for n=3
2+3(3)=11
Now for n=10
2+3(10)=32

Use this equation to solve:
\[\frac{ n }{ 2 }(a _{1}+a)\]
*Note* The reason we're solving for n=3 rather than n=1 is because we are solving for trips 3-10, not 1-10

n= the number of trips (10-3)+1
n=8

Substitute and solve.
\[8(11+32)\]
\[8(43)\]
Your answer is: 344

Answer 2

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