Question

On the first day of baseball tournament Jessie scored 2 runs. On the second day, 4 runs. On the third day, 6 runs. If this pattern continues, how many runs should Jessie score on the eighth day?

Answer 1

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: $a_n=a_1+(n-1)d$, where,

$a_n=\text{nth term of the sequence}$,

$a_1=\text{1st term of the sequence}$,

$n=\text{Number of terms of the sequence}$,

$d=\text{Common difference}$.

Since on the first day Jessie scored 2 runs, so $a_1=2$ 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,

$a_n=2+(n-1)*2$

$a_n=2+2n-2$

$a_n=2n$

Therefore, formula for nth term of sequence representing number scored by Jessie on the baseball tournament is $a_n=2n$.

Let us find the 8th term of sequence by substituting n=8 in our sequence formula.

$a_8=2*8$

$a_8=16$

Therefore, Jessie should score 16 runs on the eighth day of baseball tournament.