Exercise 1 Page 670

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= 14 and d= 9, so we can substitute these values to write the equation. a_n= 14+( n-1) 9 Let's also simplify this equation.

a_n=14+(n-1)9

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Simplify right-hand side

Distr

Distribute 9

a_n=14+9n-9

SubTerm

Subtract term

a_n=5+9n

CommutativePropAdd

Commutative Property of Addition

a_n=9n+5

To find the value of the 11th term, we substitute n= 11 into this equation and simplify.

a_n=9n+5

Substitute

n= 11

a_(11)=9( 11)+5

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Evaluate right-hand side

Multiply

Multiply

a_(11)=99+5

AddTerms

Add terms

a_(11)=104

The value of the 11th term in the sequence is 104.