Exercise 89 Page 437

Explicit rules for arithmetic sequences 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. Let's observe the other terms to determine the common difference d. 17-3 →14-3 →11-3 →8... The common difference is -3. If we substitute these two values into the explicit equation and simplify, we can find the formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

d= -3, a_1= 17

a_n= 17+(n-1)( -3)

Distr

Distribute -3

a_n=17-3n+3

AddTerms

Add terms

a_n=20- 3n

This equation can be used to find any term in the given sequence. To find a_(50), the {\color{#FD9000}{50}}^\text{th} term in the sequence, we substitute 50 for n.

a_n=20 - 3n

Substitute

n= 50

a_(50)=20 - 3( 50)

Multiply

Multiply

a_(50) = 20 - 150

SubTerm

Subtract term

a_(50) = - 130

The 50^\text{th} term in the sequence is -130.