Exercise 9 Page 212

Explicit equations for arithmetic sequences follow a specific format. a_n= a_1+( n-1) d In this form, a_1 is the first term of the sequence, d is the common difference, and a_n is the nth term. In the given sequence, the first term is a_1= 8. Let's pay close attention to the pattern in order to determine the common difference d. 8+ 8 ⟶16+ 8 ⟶24+ 8 ⟶32+ 8 ⟶... The common difference is 8. Therefore, by substituting a_1= 8 and d= 8 into the explicit equation and simplifying, we can find the formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

d= 8, a_1= 8

a_n= 8+(n-1)( 8)

Distr

Distribute 8

a_n=8+8n-8

SubTerm

Subtract term

a_n=8n

We found the equation for the nth term of the given arithmetic sequence. This equation can be used to find any term of the sequence. To find a_(25), the 25th term, we substitute 25 for n.

a_n=8n

Substitute

n= 25

a_(25)=8( 25)

Multiply

Multiply

a_(25)=200

The 25th term of the sequence is 200.