Exercise 34 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= -6. Let's observe the other terms to determine the common difference d. -6+( - 3) ⟶-9+( - 3) ⟶-12+( - 3) ⟶-15+( - 3) ⟶ ... The common difference is d= - 3. 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= -3, a_1= -6

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

Distr

Distribute -3

a_n=-6-3n+3

AddTerms

Add terms

a_n=-3 n-3

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=- 3n-3

Substitute

n= 10

a_(10)=-3( 10)-3

MultNegPos

(- a)b = - ab

a_(10)=-30-3

SubTerm

Subtract term

a_(10)=-33

The 10th term in the sequence is -33.