A large multiplex movie house has many theaters. The largest theater has 35 rows. There are 13 seats in the first row. Each row has two seats more than the previous row. How many total seats are there in this theater?
There are
seats in the theater

There are 1645 seats in the theatre.

Step-by-step explanation:

The first row has 13 seats and each row has 2 seats more than the previous one which means

13,15,17...

As the terms are increasing with the same difference, d=2 this forms an arithmetic sequence.

where

The rule for an arithmetic sequence is given by:

Putting the value of a1 and d

We have to find total seats in the theatre for that the 35th term of sequence is required as their are 35 rows.

So,

Putting n=35

Now we need to find the sum of the 35 terms

The formula for sum of arithmetic sequence is:

Hence,

There are 1645 seats in the theatre.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;