Exercise 11 Page 711

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. We are given that a_1= 9 and d= 3, so we can substitute these values to write the equation. a_n= 9+( n-1) 3 Let's also simplify this equation.

a_n=9+(n-1)3

Distr

Distribute 3

a_n=9+3n-3

SubTerm

Subtract term

a_n=6+3n

To find the value of the 14th term, we substitute n= 14 into this equation and solve for a_(14).

a_n=6+3n

Substitute

n= 14

a_(14)=6+3( 14)

Multiply

Multiply

a_(14)=6+42

AddTerms

Add terms

a_(14)=48

The 14th term in the sequence is 48.