Exercise 1 Page 575

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. 2+6 →8+6 →14+6 →20 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= 2, we can write and simplify the equation.

a_n=a_1+(n-1)d

SubstituteII

a_1= 2, d= 6

a_n= 2+(n-1) 6

Distr

Distribute 6

a_n=2+6n-6

SubTerm

Subtract term

a_n=6n-4

Solving for the nth Term

To find the value of the 10th term, we substitute n= 10 into this equation and simplify.

a_n=6n-4

Substitute

n= 10

a_n=6( 10)-4

Multiply

Multiply

a_n=60-4

SubTerm

Subtract term

a_n=56

The 10th term in the sequence is 56.