Mathematics 2016 JAMB Past Questions - Question 35: The nth term of the sequence 3, 9, 27, 81.....is

Correct Answer

B

Explanation

common ratio, r = 9/3 = 27/9= 3, a=3Hence, Tn = arsupn-1= 3x3sup3n01The given sequence 3, 9, 27, 81, ... is a geometric sequence where each term is obtained by multiplying the previous term by 3.The nth term of a geometric sequence can be found using the formula:\[a_n = a_1 \times r^{(n-1)}\]where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.In this sequence, the first term \(a_1\) is 3, and the common ratio \(r\) is 3.So, the nth term of the sequence is:\[a_n = 3 \times 3^{(n-1)}\]Therefore, the nth term of the sequence is \(3 \times 3^{(n-1)}\).