240,120,60,30....
in the sequence above eah term of after the first is 1/2 of the preceding term. whats the least of the sequne that is greater than 1?
32/15
16/15
15/8
15/4
15/2
pleaase expalin
gmat q
This topic has expert replies
-
- Legendary Member
- Posts: 559
- Joined: Tue Mar 27, 2007 1:29 am
- Thanked: 5 times
- Followed by:2 members
-
- Moderator
- Posts: 772
- Joined: Wed Aug 30, 2017 6:29 pm
- Followed by:6 members
240, 120, 80, 30 ...
Let the first term be a
a = 240
The sequence is a GP of common ratio r = $$\frac{1}{2}$$
Since, $$_{Tn}$$ = $$_{^{ar^{n-1}}}$$
The fifth term $$_{_{T_5}}$$ = 240 ( $$\left(\frac{1}{2}\right)$$) $$^{5-1}$$
240 ( $$\frac{1}{16}$$ ) = $$\frac{240}{16}$$
=15
Similarly,
$$_{T_6}$$ = 240/ $$_{^{2^5}}$$ = 7.5
$$_{^{_{T_7}}}$$ = 240/ $$_{^{_{^{2^6}}}}$$ =3.75
$$_{^{_{^{_{T_8}}}}}$$ = 240/ $$_{^{_{^{_{^{2^7}}}}}}$$ =1.857
$$_{^{_{^{_{^{_{_{_{T9}}}}}}}}}$$ = 240/ $$_{^{_{^{^{2^8}}}}}$$ = 0.9375
The sequence is ;
240, 120, 60, 30, 15, 7.5, 3.75, 1.857, 0.9395, ...
The least term greater than one is 1.857 = $$\frac{15}{8}$$
Let the first term be a
a = 240
The sequence is a GP of common ratio r = $$\frac{1}{2}$$
Since, $$_{Tn}$$ = $$_{^{ar^{n-1}}}$$
The fifth term $$_{_{T_5}}$$ = 240 ( $$\left(\frac{1}{2}\right)$$) $$^{5-1}$$
240 ( $$\frac{1}{16}$$ ) = $$\frac{240}{16}$$
=15
Similarly,
$$_{T_6}$$ = 240/ $$_{^{2^5}}$$ = 7.5
$$_{^{_{T_7}}}$$ = 240/ $$_{^{_{^{2^6}}}}$$ =3.75
$$_{^{_{^{_{T_8}}}}}$$ = 240/ $$_{^{_{^{_{^{2^7}}}}}}$$ =1.857
$$_{^{_{^{_{^{_{_{_{T9}}}}}}}}}$$ = 240/ $$_{^{_{^{^{2^8}}}}}$$ = 0.9375
The sequence is ;
240, 120, 60, 30, 15, 7.5, 3.75, 1.857, 0.9395, ...
The least term greater than one is 1.857 = $$\frac{15}{8}$$
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
After 30, we have:yvonne12 wrote:240,120,60,30....
in the sequence above eah term of after the first is 1/2 of the preceding term. whats the least of the sequne that is greater than 1?
32/15
16/15
15/8
15/4
15/2
pleaase expalin
15, 15/2, 15/4, 15/8, 15/16.
Since 15/16 is not greater than 1, we see that the smallest number in the sequence greater than 1 is 15/8.
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews