Exercise 86 Page 503

To find the 150^(th) term of the given sequence, let's start by writing its explicit formula. Looking at sequence, it seems like it might be arithmetic. Explicit rules for this type of sequence follow a specific format. a_n= a_1+( n-1) d In this form, a_1 is the first term in a given sequence, d is the common difference from one term to the next, and a_n is the {\color{#FD9000}{n}}^\text{th} term in the sequence. For this exercise, the first term is a_1= 17 and n is 150. Let's look at the other terms to determine the common difference d. 17- 12 →16 12- 12 →16- 12 →15 12... Let's substitute these values into the explicit rule and simplify to create the equation for this sequence.

a_n=a_1+(n-1)d

SubstituteII

d= -1/2, a_1= 17

a_n= 17+(n-1)( -1/2)

Distr

Distribute -1/2

a_n=17-n/2+1/2

AddTerms

Add terms

a_n=17 12 - n/2

This equation can be used to find any term in the given sequence. To find a_(150), the {\color{#FD9000}{150}}^\text{th} term in the sequence, we substitute 150 for n.

a_n=17 12 - n/2

Substitute

n= 150

a_(150)=17 12 - 150/2

Div

Divide by 2

a_(150) = 17 12-75

SubTerm

Subtract term

a_(150)=-57 12

The 150^\text{th} term in the sequence is -57 12.