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A sequence of numbers a1, a2, a3, . . . is given by the rule an^2 = an

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Math Expert
Joined: 02 Sep 2009
Posts: 50610
A sequence of numbers a1, a2, a3, . . . is given by the rule an^2 = an  [#permalink]

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05 Nov 2017, 01:10
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A sequence of numbers $$a_1$$, $$a_2$$, $$a_3$$, . . . is given by the rule $$(a_n)^2 = a_{n + 1}$$. Does 3 appear in the sequence?

(1) $$a_1 = 2$$

(2) $$a_3 = 16$$

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Joined: 02 Aug 2009
Posts: 7034
Re: A sequence of numbers a1, a2, a3, . . . is given by the rule an^2 = an  [#permalink]

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05 Nov 2017, 01:21
Bunuel wrote:
A sequence of numbers $$a_1$$, $$a_2$$, $$a_3$$, . . . is given by the rule $$(a_n)^2 = a_{n + 1}$$. Does 3 appear in the sequence?

(1) $$a_1 = 2$$

(2) $$a_3 = 16$$

hi...

$$(a_n)^2 = a_{n + 1}$$ means all numbers are increasing even POWER of same number
so to know the entire sequence, you require to know only one number in the sequence..

(1) $$a_1 = 2$$
so the numbers are $$2,2^2,2^4,2^8.....$$
3 will not come
suff

(2) $$a_3 = 16$$
again this tells us that sequence is of 2 and its even powers as 16 = 2^4
3 is not in sequence
suff

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: A sequence of numbers a1, a2, a3, . . . is given by the rule an^2 = an  [#permalink]

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11 Nov 2017, 07:28
This is a GP. a2 = a1^2, a3 = a2^2 and so on.
I. a1 = 2. Since the series is a sequence of squares of 2, therefore, 3 never comes in the picture
II. a3 = 16. a2 = 4, a1 = 2. 3 does not come
D.
Re: A sequence of numbers a1, a2, a3, . . . is given by the rule an^2 = an &nbs [#permalink] 11 Nov 2017, 07:28
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A sequence of numbers a1, a2, a3, . . . is given by the rule an^2 = an

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