• Problem:
1, 5, 25, 75, give the nth rule in the following sequence of number.
• Answer:
The given sequence has a common ratio of 5, thus, a geometric one. Common ratio can be obtained when you divide a term by its preceding term, 25 ÷ 5 = 5 and 5 ÷ 1 = 5, in which 5 is the common ratio.
However, there might be something wrong with the fourth term. The fourth term ruined the pattern. Let's say the fourth term should be 125.
To formulate a rule for the given sequence, we'll use the formula for geometric sequence.
[tex]\huge\boxed{\begin{array}{} \tt a_n=a_1r {}^{n - 1} \\ \tt a_n=1(5){}^{n - 1} \\ \blue{\tt a_n=(5) ^{n - 1}} \end{array}}[/tex]
• Thus, the nth rule for the given sequence is 5 raised to ( n - 1 ) power.
