Question

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 ?

Answer 1

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
`13+4=17` votes to 4th contestant.

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

`S_n=(n)/(2)* (a_1+a_n)`, where,

`S_n` = Sum of first n terms of sequence.

n = Number of terms of the sequence,

`a_1`= First term of sequence,

`a_n` = nth term of sequence.

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

`S_(4)=(n)/(2)* (a_1+a_4)`

`S_(4)=(4)/(2)* (5+17)`

`S_(4)=2* (22)`

`S_(4)=44`

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