Exercise 10 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) 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) + 20; a_1= - 45 We can see that 20 is the common difference and the first term is - 45. Now we have enough information to form an explicit formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

a_1= - 45, d= 20

a_n= - 45+(n-1) 20

Distr

Distribute 20

a_n = - 45 + 20n - 20

SubTerms

Subtract terms

a_n = 20n - 65