Exercise 12 Page 316

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_n=a_(n-1)+ d; & a_1= a_1 [0.8em] Explicit:& a_n= a_1+(n-1) d In these formulas, d is the common difference and a_1 is the first term. Looking at the given explicit formula, we see that we have to rewrite it a little bit in order to identify the common difference d and the value of the first term a_1.

a_n = - n + 1

FactorOut

Factor out - 1

a_n = (n-1)(- 1)

IdPropAdd

Identity Property of Addition

a_n = 0 +(n-1)(- 1)

Let's write the explicit formula a_n= 0+(n-1)( - 1) We can see that - 1 is the common difference and the first term is 0. Now we have enough information to form a recursive formula for this sequence. a_n&=a_(n-1) - 1; a_1&= 0