Exercise 3 Page 63

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 in a given sequence, d is the common difference from one term to the next, and a_n is the nth term in the sequence. For this exercise, the first term is a_1= 2.8. Let's observe the other terms to determine the common difference d. 2.8+0.6 →3.4+0.6 →4.0+0.6 →4.6... By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

d= 0.6, a_1= 2.8

a_n= 2.8+(n-1)( 0.6)

Distr

Distribute 0.6

a_n=2.8+0.6n-0.6

SubTerm

Subtract term

a_n=0.6n+2.2

This equation can be used to find any term in the given sequence. To find a_(50), the 50th term in the sequence, we substitute 50 for n.

a_n=0.6n+2.2

Substitute

n= 50

a_(50)=0.6( 50)+2.2

Multiply

Multiply

a_(50)=30+2.2

AddTerms

Add terms

a_(50)=32.2

The 50th term in the sequence is 32.2.