Question
A theater has 49 seats in the first row, 52 seats in the second row, 55 seats in the third row, and so on. How many seats are there in row 20?
Answers
GPT 3.5
The number of seats in each row forms an arithmetic sequence with a common difference of 3 (since each new row adds 3 seats).
The first term of this arithmetic sequence is 49.
The general formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Using this formula, we can find the number of seats in the 20th row:
a20 = 49 + (20 - 1) * 3
= 49 + 19 * 3
= 49 + 57
= 106
Therefore, there are 106 seats in row 20.
The first term of this arithmetic sequence is 49.
The general formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Using this formula, we can find the number of seats in the 20th row:
a20 = 49 + (20 - 1) * 3
= 49 + 19 * 3
= 49 + 57
= 106
Therefore, there are 106 seats in row 20.