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
chelleanne
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 | |
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.
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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.