Exercise 33 Page 215

Explicit equations for arithmetic sequences follow a specific format. a_n= a_1+(n-1) d In this form, a_1 is the first term of the sequence, d is the common difference, and a_n is the nth term. In the given arithmetic sequence, the first term is a_1= -5. Let's observe the other terms to determine the common difference d. -5+ 1 ⟶-4+ 1 ⟶-3+ 1 ⟶-2+ 1 ⟶ ... The common difference is d= 1. By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

d= 1, a_1= -5

a_n= -5+(n-1)( 1)

IdPropMult

Identity Property of Multiplication

a_n=-5+n-1

SubTerms

Subtract terms

a_n=n-6

This equation can be used to find any term in the given sequence. To find a_(10), the 10th term in the sequence, we substitute 10 for n.

a_n=n-6

Substitute

n= 10

a_(10)= 10-6

SubTerm

Subtract term

a_(10)=4

The 10th term in the sequence is 4.