Exercise 24 Page 319

The explicit formula of an arithmetic sequence combines the information provided by the two equations of the recursive form into a single equation. Recursive: a_1&= a_1, a_n&=a_(n-1)+ d; [0.8em] Explicit: a_n&= a_1+(n-1) dIn these formulas, d is the common difference and a_1 is the first term. Looking at the given recursive formula, we can identify the common difference d and the value of the first term a_1. a_1&=8; a_n=a_(n-1)- 12 & ⇕ a_1&= 8; a_n=a_(n-1)+( - 12) We can see that - 12 is the common difference and the first term is equal 8. Now we have enough information to form an explicit formula for this sequence.