Jessica is voting for dancers in a contest. She votes for 5 times for the first contestant 2nd contestant 9 times and the third contestant 13 times if she continues the pattern how many total votes will Jessica cast for the first four contestants explain ?

We have been given that Jessica is voting for dancers in a contest. She votes for 5 times for the first contestant 2nd contestant 9 times and the third contestant 13 times.

We can see that Jessica votes to next contestant 4 votes more than previous contestant, so number of votes cast by Jessica to contestants form an arithmetic sequence as: 5, 9, 13,..

Since the common difference of our sequence is 4, so Jessica will cast [tex]13+4=17[/tex] votes to 4th contestant.

We will use arithmetic sequence sum formula to solve our problem.

[tex]S_n=\frac{n}{2}\times (a_1+a_n)[/tex], where,

[tex]S_n[/tex] = Sum of first n terms of sequence.

n = Number of terms of the sequence,

[tex]a_1[/tex]= First term of sequence,

[tex]a_n[/tex] = nth term of sequence.

Upon substituting our given values in above formula we will get,

[tex]S_{4}=\frac{n}{2}\times (a_1+a_4)[/tex]

[tex]S_{4}=\frac{4}{2}\times (5+17)[/tex]

[tex]S_{4}=2\times (22)[/tex]

[tex]S_{4}=44[/tex]

Therefore, Jessica will cast 44 votes the first four contestants.