Question

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 the number of total jumps from her second to tenth trips.

Answer 1

@amistre64 @John_ES

Answer 2

what have you considered in this?

Answer 3

when i=1, it says she did 6 .... there are only 2 options that gives us a 6 when i = 1

Answer 4

they all = 6

Answer 5

.... well yeah, if you want to be correct. I was thinking ahead to when i=2 we need 6+2 = 8 :)

Answer 6

2i+4 gives us 1=6, 2=8, ...

so we need a way to pick between the first 2 options

Answer 7

so, find 2(6)+4...?

Answer 8

no, the simplest way to approach this is just to calculate all the i's

2(2)+4
2(3)+4
2(4)+4
2(5)+4
2(6)+4
2(7)+4
2(8)+4
2(9)+4
2(10)+4
---------
2(2+3+4+5+6+7+8+9+10) +4(9)

2(2+10)(9)
---------- + 4(9)
2


9(2+10+4) = 9(16)

Answer 9

=144..? is that it?

Answer 10

if you know how to run summations properties ... which the content of your replies indicate that you may not ... we could have gone:
\[\sum_{2}^{10}2i+4\]
\[\sum_{2-1}^{10-1}2(i+1)+4\]
\[\sum_{1}^{9}2i+6\]
\[2\sum_{1}^{9}i+6\sum_{1}^{9}\]
\[2\frac{9(1+9)}{2}+6(9)\]
\[9(10)+6(9)=9(16)\]

Answer 11

144 is it yes

Answer 12

oh, thanks... I didn't think it was that easy.

Answer 13

youre welcome