Geometric Progression

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Tue Aug 23, 2011 4:45 am

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

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top_business_2011: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Wed Sep 03, 2008 11:18 pmFollowed by: 1 member; Thanked: 5 times

by top_business_2011 » Tue Aug 23, 2011 7:33 am

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

Here, using the geometric progression formula may come in handy.

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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sunilrawat: Master | Next Rank: 500 Posts; Posts: 112; Joined: Sun Jun 13, 2010 9:20 am; Thanked: 5 times; GMAT Score:640

by sunilrawat » Tue Aug 23, 2011 7:36 am

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

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue Aug 23, 2011 8:30 am

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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czarczar: Master | Next Rank: 500 Posts; Posts: 106; Joined: Fri Feb 05, 2010 9:39 amFollowed by: 1 member; Thanked: 4 times

by czarczar » Wed Aug 24, 2011 8:54 am

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

Appreciated , I did not notice that r can also be -2 .

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Wed Sep 28, 2011 7:55 am

32 = (1/32)* r^10

gives r= 2

6th term = 1/32 * r^5 = 1

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