Exercise 25 Page 579

We want to find the missing terms of the given arithmetic sequence. 10, a_2, a_3, a_4, - 20, ... To accomplish this, we will use the fact that the arithmetic mean of the first and fifth terms is the third term. To find the arithmetic mean of two numbers, we add them and divide by 2. a_3=a_1+a_5/2 Let's substitute 10 for a_1 and - 20 for a_5 in the above equation.

a_3=a_1+a_5/2

SubstituteII

a_1= 10, a_5= - 20

a_3=10+( - 20)/2

▼

Evaluate right-hand side

AddNeg

a+(- b)=a-b

a_3=- 10/2

MoveNegNumToFrac

Put minus sign in front of fraction

a_3=- 10/2

CalcQuot

Calculate quotient

a_3=- 5

Now we can use the fact that a_1= 10, a_3= - 5, and a_5= - 20 to find a_2 and a_4 by calculating two more arithmetic means.

a_n=a_(n-1)+a_(n+1)/2
a_2=a_1+a_3/2	a_4=a_3+a_5/2
a_2=10+( - 5)/2	a_4=- 5+( - 20)/2
a_2=5/2	a_4=- 25/2
a_2=2.5	a_4=- 12.5

Finally, we can complete the sequence. ccccc a_1 & a_2 & a_3 & a_4 & a_5 [0.8em] 10 & 2.5 & - 5 & - 12.5 & - 20