Exercise 13 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. 1+7 →8+7 →15+7 →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= 7 and the first term a_1= 1, we can write and simplify the equation.

a_n=a_1+(n-1)d

SubstituteII

a_1= 1, d= 7

a_n= 1+(n-1)( 7)

Distr

Distribute 7

a_n=1+7n-7

SubTerm

Subtract term

a_n=7n-6

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)
7* 9-6	7* 10-6
63-6	70-6
57	64