The correct answers are:
[tex] \Sigma_{n=4}^{12} 6+2(n-1)
\\
\\=180 [/tex]
Explanation:
Since she is adding two more jumps every time she goes down hill, this is an arithmetic sequence. The general form of an arithmetic sequence is
[tex] a_n=a_1+d(n-1),
\\
\text{where } a_n \text{represents the nth term, } a_1 \text{represents the first term, and n represents the term number} [/tex]
Since we want the number of jumps on her 4th through 12th trips, we will set n in the summation from 4 to 12. n=4 goes at the bottom of Σ and 12 goes at the top, to represent the values we are interested in.
Beside this, we write our general form. The first term is 6 and d, the common difference, is 2. This gives us 6+2(n-1) beside the summation:
[tex] \Sigma_{n=4}^{12} 6+2(n-1) [/tex]
To evaluate this, we substitute the values 4, 5, 6, 7, 8, 9, 10, 11 and 12 in for n, adding all of the values together:
6+2(4-1)+6+2(5-1)+6+2(6-1)+6+2(7-1)+6+2(8-1)+6+2(9-1)+6+2(10-1)+6+2(11-1)+6+2(12-1)
=6+6+6+8+6+10+6+12+6+14+6+16+6+18+6+20+6+22
=180
