Exercise 27 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_n=a_(n-1)+ d; & a_1= a_1 [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_n=a_(n-1)+ 17; a_1= 4 We can see that 17 is the common difference and the first term is 4. Now we have enough information to form an explicit formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

a_1= 4, d= 17

a_n= 4+(n-1) 17

Distr

Distribute 17

a_n = 4 + 17n - 17

SubTerms

Subtract terms

a_n = 17n - 13