Exercise 37 Page 205

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= 10. Let's observe the other terms to determine the common difference d. 10+( - 10) ⟶0+( - 10) ⟶-10+( - 10) ⟶-20 +( - 10) ⟶ ... The common difference is d= - 10. 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= -10, a_1= 10

a_n= 10+(n-1)( -10)

Distr

Distribute -10

a_n=10-10n+10

AddTerms

Add terms

a_n=-10 n+20

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=-10 n+20

Substitute

n= 10

a_(10)=-10( 10)+20

MultNegPos

(- a)b = - ab

a_(10)=-100+20

AddTerms

Add terms

a_(10)=-80

The 10th term in the sequence is -80.