Answer:
Students got 3 signature on the first day.
Step-by-step explanation:
We are given the following in the question:
The number of signatures they get each day is 3 times as many as the day before.
Thus, the number of signature forms a G.P with common ratio, r = 3.
The expression 3 to the 6th power represents the number of signatures they got on the sixth day. Thus we can write:
[tex]a_6 = 3^6[/tex]
The [tex]n^{th}[/tex] term in a G.P is given by
[tex]a_n = a_1r^{n-1}[/tex]
where [tex]a_1[/tex] is the first term in the G.p
Putting values, we get,
[tex]3^6 = a_1(3)^{6-1}\\3^6 = a_1(3)^5\\\Rightarrow a_1 = 3[/tex]
Thus, the first term of G.P is 3.
Hence, students got 3 signature on the first day.
