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Sequence

by smackmartine » Sat Jun 18, 2011 11:06 pm
Please time yourself..

The infinite sequence A1,A2,...An is such that A1=x,A2=y,A3=z,A4=3 and An=A(n-4) for n>4 . What is the sum of the first 98 terms of sequence ?

1)x=5
2)y+z =2
Last edited by smackmartine on Sat Jun 18, 2011 11:34 pm, edited 3 times in total.
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by Anurag@Gurome » Sat Jun 18, 2011 11:10 pm
smackmartine wrote:Please time yourself..

The infinite sequence A1,A2,...An is such that A1=x,A2=y,A3=z,A4=3 and An=An-4 for n>4 . What is the first 98 terms of sequence ? ...
Can you please check the red part and confirm whether the question is asking for the first 98 terms or the sum of first 98 terms?
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by smackmartine » Sat Jun 18, 2011 11:21 pm
Anurag@Gurome wrote:
smackmartine wrote:Please time yourself..

The infinite sequence A1,A2,...An is such that A1=x,A2=y,A3=z,A4=3 and An=An-4 for n>4 . What is the first 98 terms of sequence ? ...
Can you please check the red part and confirm whether the question is asking for the first 98 terms or the sum of first 98 terms?
Sorry Aurag, I have edited the question!!
Last edited by smackmartine on Sat Jun 18, 2011 11:21 pm, edited 1 time in total.
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by Anurag@Gurome » Sat Jun 18, 2011 11:21 pm
smackmartine wrote:The infinite sequence A1,A2,...An is such that A1=x,A2=y,A3=z,A4=3 and An=An-4 for n>4 . What is the sum of the first 98 terms of sequence ?

1)x=5
2)y+z =2
I assume the correct formula is A(n) = A(n - 4)
Therefore, A(5) = x, A(6) = y, A(7) = z, A(8) = 3 ... etc
Hence, the terms are actually a repeating sequence of x, y, z, and 3.

Sum of first 98 terms = (x + y + z + 3) + (x + y + z + 3) + [24 times] ... + x + y = 24(x + y + z + 3) + (x + y)

Statement 1: No information about y and z.

Not sufficient

Statement 2: No information about x.

Not sufficient

1 & 2 Together: Sum = 24(x + y + z + 3) + (x + y) = 24*(5 + 2 + 3) + (5 + y) = (245 + y)
We don't know the value of y.

Not sufficient

The correct answer is E.
Last edited by Anurag@Gurome on Sun Jun 19, 2011 5:57 am, edited 1 time in total.
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by amit2k9 » Sun Jun 19, 2011 2:28 am
a gives no clue of y and z. not sufficient.

b gives value for x.not sufficient.

a+b as 98 is divisible by 7. the sum of first 7 terms multiplied by 28 will suffice.

sufficient. C it is.
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by HSPA » Sun Jun 19, 2011 4:44 am
Hi Anurag sir,
I small help..
How to avoid my confusion for the 98th term
A1 = x A2= y, A3= z, A4 = 3..
I got sum of 98 terms as
24(x+y+z+3)+(x+y)

what is the 98th term is it y or Z or X??? I know it sounds silly as I got answer as E and not C.

Anurag@Gurome wrote:
smackmartine wrote:The infinite sequence A1,A2,...An is such that A1=x,A2=y,A3=z,A4=3 and An=An-4 for n>4 . What is the sum of the first 98 terms of sequence ?

1)x=5
2)y+z =2
I assume the correct formula is A(n) = A(n - 4)
Note that we can determine the values of A(5), A(6), ..., A(97), and A(98) using the given formula. And we know the the value of A(4). But we don't know the values of A(1), A(2), and A(3).

Sum of first 98 terms = (x + y + z + A(4) + A(5) + ... + A(98))
The blue part is known. Hence, we need to know the sum of x, y, and z.

Only statement 1 & 2 together gives us the sum o x, y, and z.

The correct answer is C.
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by Frankenstein » Sun Jun 19, 2011 5:10 am
HSPA wrote: A1 = x A2= y, A3= z, A4 = 3..
I got sum of 98 terms as
24(x+y+z+3)+(x+y)

what is the 98th term is it y or Z or X??? I know it sounds silly as I got answer as E and not C.
Hi,
98th term is y.
IMO, you are correct. I feel E is correct.
Please post OA.
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by Anurag@Gurome » Sun Jun 19, 2011 5:52 am
Thanks HSPA and Frankenstein.
The blue part is not known as some of them will be equal to x or y or z. The format of the formula (An = An - 4) tricked me.

Editing the reply.
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by smackmartine » Sun Jun 19, 2011 11:06 am
OA E
Thanks guys. I got tricked too.
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by lunarpower » Wed Jun 29, 2011 12:41 am
of note --

if you change "98" (in the question prompt) to either "97" or "99", then the correct answer becomes (c). be sure that you know why.
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