Exercise 64 Page 593

We want to write an explicit formula for the geometric sequence. To do so, we will start by recalling the general formula for a geometric sequence. a_n=a_1r^(n-1) Now we will substitute the given values, a_1=3 and r= 32, into this formula. a_n= 3 ( 3/2)^(n-1) We already know that a_1=3. To generate the second term, a_2, we will substitute 2 for n.

a_n=3(3/2)^(n-1)

Substitute

n= 2

a_2=3(3/2)^(2-1)

▼

Evaluate right-hand side

SubTerm

Subtract term

a_2=3(3/2)^1

ExponentOne

a^1=a

a_2=3(3/2)

MoveLeftFacToNum

a*b/c= a* b/c

a_2=3 * 3/2

Multiply

Multiply

a_2=9/2

We will follow the same procedure to generate a_3.

a_n=3(3/2)^(n-1)

Substitute

n= 3

a_3=3(3/2)^(3-1)

▼

Evaluate right-hand side

SubTerm

Subtract term

a_3=3(3/2)^2

CalcPow

Calculate power

a_3=3(9/4)

MoveLeftFacToNum

a*b/c= a* b/c

a_3=3 * 9/4

Multiply

Multiply

a_3=27/4