Question

Students are getting signatures for a petition to increase sports activities at the community center. The number of signatures they get each day is 3 times as many as the day before. The expression 3^6 represents the number of signatures they got on the sixth day. How many signatures did they get on the first day?

Answer 1

The students got 3 signatures on first day.

Explanation:

We are given the following in the question:

The number of signatures students get each day is 3 times as many as the day before.

Thus, the number of signatures form a geometric progression with common ratio 3.

`r = 3`

Number of signatures on sixth day =
`3^6`

`n^(th)` term in a geometric progression is given by:

`a_n = ar^(n-1)`

where a is the first term of the series and r is the common ratio.

`a_6 = 3^6\\3^6 = ar^(5)\\3^6 = a(3)^5\\a = 3`

Thus, the first term of geometric progression is 3.

Thus, the students got 3 signatures on first day.