Question

describe the pattern, write the next term, and write a rule for the n th term of the sequence.
1,7,13,19, ...
describe the pattern.
6 - 5, 6 - 4, 6 - 3, 6 - 2
6^1 - 5, 6^2 - 5, 6^3 - 5, 6^4 - 5
6(1) - 5, 6(2) - 5, 6(3) - 5, 6(4) - 5
6(1) + 1, 6(2) + 2, 6(3) + 3, 6(4) + 4
the next term is 25
the rule for the n th term is a_n = \square.

Explanation:

Step1: Analyze the sequence pattern

The given sequence is 1, 7, 13, 19, ... We can see that each term is generated by the formula \(6n - 5\) (from the pattern \(6(1)-5, 6(2)-5, 6(3)-5, 6(4)-5\)). For \(n = 1\), \(6(1)-5=1\); for \(n = 2\), \(6(2)-5 = 7\); for \(n=3\), \(6(3)-5=13\); for \(n = 4\), \(6(4)-5 = 19\).

Step2: Determine the nth term formula

From the pattern analysis, the nth term \(a_n\) of the sequence follows the rule \(a_n=6n - 5\).

Answer:

\(6n - 5\)