Exercise 6 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= 8. Let's observe the other terms to determine the common difference d. 8- 6 →2- 6 →- 4- 6 →- 10... 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= - 6, a_1= 8

a_n= 8+(n-1)( - 6)

Distr

Distribute - 6

a_n=8-6n+6

AddTerms

Add terms

a_n=- 6n+14

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=- 6n+14

Substitute

n= 50

a_(50)=- 6( 50)+14

Multiply

Multiply

a_(50)=- 300+14

AddTerms

Add terms

a_(50)=- 286

The 50th term in the sequence is - 286.