Exercise 2 Page 439

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 in a given sequence, d is the common difference from one term to the next, and a_n is the nth term in the sequence. For this exercise, the first term is a_1= - 29. Let's observe the other terms to determine the common difference d. - 29+17 →- 12+17 →5+17 →22... 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= 17, a_1= - 29

a_n= - 29+(n-1)( 17)

Distr

Distribute 17

a_n=- 29+17n-17

SubTerm

Subtract term

a_n=17n-46

This equation can be used to find any term in the given sequence. To find a_(50), the 50th term in the sequence, we substitute 50 for n.

a_n=17n-46

Substitute

n= 50

a_(50)=17( 50)-46

Multiply

Multiply

a_(50)=850-46

SubTerm

Subtract term

a_(50)=804

The 50th term in the sequence is 804.