Exercise 5 Page 63

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= 26. Let's observe the other terms to determine the common difference d. 26- 4 →22- 4 →18- 4 →14... 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= - 4, a_1= 26

a_n= 26+(n-1)( - 4)

Distr

Distribute - 4

a_n=26-4n+4

AddTerms

Add terms

a_n=- 4n+30

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=- 4n+30

Substitute

n= 50

a_(50)=- 4( 50)+30

Multiply

Multiply

a_(50)=- 200+30

AddTerms

Add terms

a_(50)=- 170

The 50th term in the sequence is - 170.