Question

The first term of an arithmetic sequence is 42. The rule an = an-1 + 8 can be used to find the next term of the sequence.

Answer 1

Here, a(n) = a(n-1) + 8
As the common difference = 8

We know, a(n) = a + (n - 1)d

Substitute the known values, 
a(n) = 42 + (n - 1)8
a(n) = 42 + 8n - 8
a(n) = 8n + 34

In short, Your explicit rule would be: 8n + 34

Hope this helps!

Answer 2

The rule shows that each term is 8 more than the previous term, so the common difference is 8.The explicit formula of an arithmetic sequence is the initial term plus (n – 1)d.The explicit rule for this function can be found by substituting 42 for a1 and 8 for d.The explicit rule for the sequence is  42 + (n – 1)8.