If the first term of a geometric progression is 1/32 and 11th term is 32, what is the 6th term?
Don't have an OA or the answer choices. Detailed explanations would be appreciated. Thanks
Geometric Progression
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Here, using the geometric progression formula may come in handy.knight247 wrote:If the first term of a geometric progression is 1/32 and 11th term is 32, what is the 6th term?
Don't have an OA or the answer choices. Detailed explanations would be appreciated. Thanks
Gn = G1[r^(n-1)], Where, Gn= the nth. term
r= common ratio, G1= the first term
n= the total number of terms under consideration.
Accordingly,
G11 = G1[r^10]
32 = [1/32][r^10]
32 * 32 = r^10
2^5 *2^5 = r^10
2^10 = r^10
r=2
Hence, G6= G1[r^5]
= [1/32][2^5]
= 1.
Therefore, the answer is 1.
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let 'a' be the first term and 'r' be the common ratio
nth term = ar^(n-1)
11th term = 32
1/32*r^(11-1) = 32
r = 2.
putting in formula above,
6th term = 1/32*2^(6-1)= 1
nth term = ar^(n-1)
11th term = 32
1/32*r^(11-1) = 32
r = 2.
putting in formula above,
6th term = 1/32*2^(6-1)= 1
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Hi,
Just to add to the above posts, r can be -2 or +2. So, 6th term will be either -1 or +1.
a = 1/32
ar^10 = 32
So, a^2*r^10 = 1 =>(ar^5)^2 = 1
So, Sixth term, ar^5 = -1 or +1
Just to add to the above posts, r can be -2 or +2. So, 6th term will be either -1 or +1.
a = 1/32
ar^10 = 32
So, a^2*r^10 = 1 =>(ar^5)^2 = 1
So, Sixth term, ar^5 = -1 or +1
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Appreciated , I did not notice that r can also be -2 .Frankenstein wrote:Hi,
Just to add to the above posts, r can be -2 or +2. So, 6th term will be either -1 or +1.
a = 1/32
ar^10 = 32
So, a^2*r^10 = 1 =>(ar^5)^2 = 1
So, Sixth term, ar^5 = -1 or +1
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32 = (1/32)* r^10
gives r= 2
6th term = 1/32 * r^5 = 1
gives r= 2
6th term = 1/32 * r^5 = 1
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