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 ?

44 votes.

Step-by-step explanation:

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 votes to 4th contestant.

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

, where,

= Sum of first n terms of sequence.

n = Number of terms of the sequence,

= First term of sequence,

= nth term of sequence.

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

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

a negative exponent is translated as follows:

so, we have