I need to find the rule of the sequence.
n 2 3 4 5
t(n) 75 1875 46875 1171875
I know the bottom is times 25, but I don't get how to do a rule that is t(n)=
Well, you have the rule, so you know that
t(1) = 3*25
t(n+1) = t(n)*25
so, t(n) = 3*25^n
To find the rule of a sequence, you need to identify the relationship between the given terms. In this case, it seems that the terms are multiplied by 25 as you mentioned. Let's break down the pattern step by step:
Starting with term t(2) = 75, notice that to get the next term, t(3), we multiply t(2) by 25:
t(3) = t(2) * 25 = 75 * 25 = 1875
Similarly, to get t(4), we multiply t(3) by 25:
t(4) = t(3) * 25 = 1875 * 25 = 46875
And to get t(5), we multiply t(4) by 25:
t(5) = t(4) * 25 = 46875 * 25 = 1171875
From these examples, it appears that each term is obtained by multiplying the previous term by 25. So, the rule for this sequence can be expressed as:
t(n) = t(n-1) * 25
This means that to find any term (t(n)), you should multiply the previous term (t(n-1)) by 25.