Exercise 113 Page 297

We already know that these are arithmetic sequences, which means we can write both of them in a linear format. t(n)=mn+t(0) In this equation, m is the line's slope and t(0) is the zero term.

Coryn's sequence

For Coryn's sequence we know two consecutive terms, (2,4) and (3,5). Since these are consecutive terms, we can determine the value of m by finding the difference between 4 and 5.

The value of m is 1. Finally, we have to find the zero term. We can do that by substituting any of the points in the equation.

t(n)=n+t(0)

Substitute

n= 2

t( 2)= 2+t(0)

Substitute

t(2)= 4

4=2+t(0)

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Solve for t(0)

SubEqn

LHS-2=RHS-2

2=t(0)

RearrangeEqn

Rearrange equation

t(0)=2

We can write the first equation. t(n)=n+2

Leah's sequence

For Leah's sequence we do not have consecutive terms. Therefore, to find the value of m we should use the Slope Formula.

m = y_2 - y_1/x_2 - x_1

SubstitutePoints

Substitute ( 0,3) & ( 3,2)

m = 2 - 3/3 - 0

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Simplify right-hand side

SubTerms

Subtract terms

m = - 1/3

MoveNegNumToFrac

Put minus sign in front of fraction

m = - 1/3

The value of m is - 13. Finally, we have to find the zero term. However, from the points ( 0,3), we already know that the zero term is t( 0)= 3 With this information we can write the second equation. t(n)=- 1/3n+3