Exercise 14 Page 579

To begin, let's observe the given terms in the sequence to determine the value of the first term as well as the common difference. 4+6 →10+6 →16+6 →22 We can use this information to write an equation for the nth term of the sequence.

Writing the Equation

Explicit equations for the nth term of an arithmetic sequence follow a certain format. a_n= a_1+( n-1) d In this form, a_1 is the first term in the sequence, d is the common difference, and n is the position of the desired term in the sequence. Using the common difference d= 6 and the first term a_1= 4, we can write and simplify the equation.

a_n=a_1+(n-1)d

SubstituteII

a_1= 4, d= 6

a_n= 4+(n-1)( 6)

Distr

Distribute 6

a_n=4+6n-6

SubTerm

Subtract term

a_n=6n-2

Solving for the nth Term

To find the value of the 9th and 10th term, we substitute n= 9 and n= 10 into this equation and solve for a_n.

a_9	a_(10)
6* 9-2	6* 10-2
54-2	60-2
52	58