Answer:
16 runs.
Step-by-step explanation:
We have been given that on the first day of baseball tournament Jessie scored 2 runs. On the second day, 4 runs. On the third day, 6 runs.
We can see that runs scored by Jessie form an arithmetic sequence, where each successive term is 2 more than the previous term.
Since we know that formula for nth term of an arithmetic sequence is: [tex]a_n=a_1+(n-1)d[/tex], where,
[tex]a_n=\text{nth term of the sequence}[/tex],
[tex]a_1=\text{1st term of the sequence}[/tex],
[tex]n=\text{Number of terms of the sequence}[/tex],
[tex]d=\text{Common difference}[/tex].
Since on the first day Jessie scored 2 runs, so [tex]a_1=2[/tex] and difference between two consecutive terms is 2 (4-2=2), so d will be 2.
Upon substituting our values in arithmetic sequence formula we will get,
[tex]a_n=2+(n-1)*2[/tex]
[tex]a_n=2+2n-2[/tex]
[tex]a_n=2n[/tex]
Therefore, formula for nth term of sequence representing number scored by Jessie on the baseball tournament is [tex]a_n=2n[/tex].
Let us find the 8th term of sequence by substituting n=8 in our sequence formula.
[tex]a_8=2*8[/tex]
[tex]a_8=16[/tex]
Therefore, Jessie should score 16 runs on the eighth day of baseball tournament.
