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

Answer:

The students got 3 signatures on first day.

Step-by-step 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.