Exercise 40 Page 279

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 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(n)=A(n-1)+ 3; A(1)= 6 We can see that 3 is the common difference and the first term is 6. Now we have enough information to form an explicit formula for this sequence.

A(n)=A(1)+(n-1)d

SubstituteII

A(1)= 6, d= 3

A(n)= 6+(n-1)( 3)