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Sequence question

by Cheese12 » Sat Sep 24, 2011 2:56 am
In sequence Q, the first number is , and each subsequent number in the sequence is determined by doubling the previous number and then adding 2. How many times does the units' digit 8 appear in the first 15 numbers of the sequence?

A)7
B)8
C)10
D)12
E)13



E

Please explain your answer... need help with this one.. thanks!
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by cans » Sat Sep 24, 2011 3:42 am
f(n)=2f(n-1)+2=2(f(n-1)+1)
for unit number 8, f(n-1)+1 should end either in 9 or in 4.
thus f(n-1) should end in 8 or 3.
f(1)=1,f(2)=3,f(3)=8
now as f(3) ends in 8, f(4) will end in 8 and thus f(5) will also end in 8 and so on....
thus till f(15), 13
IMO E
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by Cheese12 » Sat Sep 24, 2011 5:09 am
cans wrote:f(n)=2f(n-1)+2=2(f(n-1)+1)
for unit number 8, f(n-1)+1 should end either in 9 or in 4.
thus f(n-1) should end in 8 or 3.
f(1)=1,f(2)=3,f(3)=8
now as f(3) ends in 8, f(4) will end in 8 and thus f(5) will also end in 8 and so on....
thus till f(15), 13
IMO E

I am sorry, I missed out something in my question..

"In sequence Q, the first number is 1/2 "

so .... if this information is given.. is plugging in good ? .. how to start of with this question ?
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by shankar.ashwin » Sat Sep 24, 2011 5:20 am
Just list down the numbers;

1st : 1/2
2nd : 3
3rd : 8
4th : 18 (Now you know 8*2 =16, so adding 2 will always end in 8)

So from the 3rd to 15th term all will end in 8.

Thats 13 terms
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