Exercise 35 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= 12. Let's observe the other terms to determine the common difference d. 12+ 12 ⟶1+ 12 ⟶1 12+ 12 ⟶2 + 12 ⟶ ... The common difference is d= 12. 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= 1/2, a_1= 1/2

a_n= 1/2+(n-1)( 1/2)

Distr

Distribute 1/2

a_n=1/2+1/2n-1/2

SubTerm

Subtract term

a_n=1/2n

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=1/2n

Substitute

n= 10

a_(10)=1/2( 10)

MoveRightFacToNumOne

1/b* a = a/b

a_(10)=10/2

CalcQuot

Calculate quotient

a_(10)=5

The 10th term in the sequence is 5.