If a5= 48 qnd a17=196608 are the terms of a goemetric sequence find a32

0  Views: 535 Answers: 2 Posted: 11 years ago
Tags:

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

country bumpkin

As Bob said, Oh come on! (*~*)
Your knowledge of math is amazing. My son is starting college in a couple of months and he's dreading the math course because he always had so much trouble understanding math.
chelleanne

I'm refreshing my memory by looking at these kids math homework. Tell your son that he can find math help by going on YouTube. Math tutors/teachers put up videos with math problems and explanation on solving for all types of math problems.
country bumpkin

I'll let him know. Thanks (*~*)

Oh, come on.

### Top contributors in Uncategorized category

ROMOS
Karma: 1101K

Colleen
Karma: 953K

country bumpkin
Karma: 838K

Benthere