2 Answers

a5 = 48
a17 = 196,608
a32 = ?

Geometric Formula: an = a1*r^n-1
a1 = 1st term
r = common ratio
n = sequence term you're finding

Write two equations using the 5th and 32nd terms from the formula.

Equation 1:

a5 = [ a1*r^5-1 = 48]
a5 = a1*r^4 = 48

Equation 2:

a17 = [ a1*r^17-1 = 196,608 ]
a17 = a1*r^16 = 196,608

Divide equation 2 by equation 1 to find common ratio.

a1*r^16 = 196,608 / a1*r^4 = 48

r^12 = 4096
r = +-2

Find the 1st term using either equation.

a1*r^4 = 48

16a1/16 = 48/16

a1 = 3

Now, find the 32nd term. There will be two answers.

an = a1*r^n-1
a32 = 3*2^32-1
a32 = 3(2)^31
a32 = 3(2,147,483,648)
a32 = 6,442,450,944

a32 = 3*-2^32-1
a32 = 3(-2)^31
a32 = 3(-2,147,483,648)
a32 = -6,442,450,944

Check: an = a1*r^n-1 > common ratio is +-2

a1 = 3

a1 = 3(2)^1-1
a1 = 3(2)^0
a1 = 3(1)
a1 = 3

a1 = 3(-2)^1-1
a1 = 3(-2)^0
a1 = 3(1)
a1 = 3



a5 = 48

a5 = 3(2)^5-1
a5 = 3(2)^4
a5 = 3(16)
a5 = 48

a5 = 3(-2)^5-1
a5 = 3(-2)^4
a5 = 3(16)
a5 = 48

a17 = 196,608

a17 = 3(2)^17-1
a17 = 3(2)^16
a17 = 3(65,536)
a17 = 196,608

a17 = 3(-2)^17-1
a17 = 3(-2)^16
a17 = 3(65,536)
a17 = 196,608

9 years ago. Rating: 3
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Oh, come on.   

12 years ago. Rating: 2
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