Question

Consider the expression un = 2n – 1. This states that the nth term of the sequence is given by the rule 2n – 1. When we substitute 1, 2, 3, ... for n in the expression 2n – 1, we get u1 = 2 × 1 – 1 = 1, u2 = 2 × 2 – 1 = 3, u3 = 2 × 3 – 1 = 5, etc. Thus, un = 2n – 1 is the explicit rule for the nth term of the sequence of odd numbers.

Consider the sequence that is generated by the explicit formula sn = 5n – 2. Can you write the first 6 terms of this sequence? What is the 100th term? The 1000th term? Let us check if the numbers 308 and 473 are terms of this sequence.