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.

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.