Exercise 5 Page 691

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= 10 and d= - 5, so we can substitute these values to write the equation. a_n= 10+( n-1) (- 5) Let's also simplify this equation.

a_n=10+(n-1)(- 5)

Distr

Distribute - 5

a_n=10-5n+5

AddTerms

Add terms

a_n=15-5n

To find the value of the 9th term, we substitute n= 9 into this equation and solve for a_9.

a_n=15-5n

Substitute

n= 9

a_9=15-5( 9)

Multiply

Multiply

a_9=15-45

SubTerm

Subtract term

a_9=- 30

The 9th term in the sequence is - 30.