Exercise 72 Page 577

We are given two terms of an arithmetic sequence. a_4=-2.4 and a_6=2 With the information provided, we want to find the common difference d and the first term a_1. Recall that the common difference is the difference between any two consecutive terms. Since the terms we are given are not consecutive, we will divide their difference by the difference of their positions.

d=a_6-a_4/6-4

SubstituteII

a_6= 2, a_4= -2.4

d=2-( -2.4)/6-4

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Evaluate right-hand side

SubNeg

a-(- b)=a+b

d=4.4/2

CalcQuot

Calculate quotient

d=2.2

Now that we know that d= 2.2, we can write a partial equation of the explicit formula for our arithmetic sequence. a_n=a_1+(n-1) d ⇕ a_n=a_1+(n-1)( 2.2) We will use this formula to find the first term a_1. To do so, we can use any of the given terms. Let's use a_6=2. Be aware that for this term the value of n is 6.

a_n=a_1+(n-1)(2.2)

Substitute

n= 6

a_6=a_1+( 6-1)(2.2)

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Simplify

SubTerms

Subtract terms

a_6=a_1+5(2.2)

Multiply

Multiply

a_6=a_1+11

Substitute

a_6= 2

2=a_1+11

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Solve for a_1

SubEqn

LHS-11=RHS-11

- 9=a_1

RearrangeEqn

Rearrange equation

a_1=- 9