In a certain sequence, when you subtract the Mth element from the (M-1

Question

In a certain sequence, when you subtract the Mth element from the (M-1)th element, you get twice the Mth element (M is any positive integer). What is the fourth element of this sequence?

(1) The first element of the sequence is 1.
(2) The third element of the sequence is 1/9.

DavidTutorexamPAL · Answer

Since the given rule tells us how to calculate one element in a sequence based on the one before/after it, then to know the value of the fourth element, all we need to know is the value of one of the elements.
We'll look for statements that give us this information, a Logical approach.

(1) gives us the first element and is sufficient.
(2) gives us the third element and is sufficient.

(D) is our answer.

Note that you don't actually need to calculate that the given rule is 'the Mth element is 1/3 the (M-1)th element' in order to solve the above.

Bunuel · Answer

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Sangam1994 · Answer

Someone can explain me the question.. I think so there is a flaw in the question

dabaobao · Answer

Solution

b1 - b2 = 2b2
b1 = 3b2
b2/b1 = 1/3 => Common Ratio

Need: Any term in sequence

1) b1 = 1 
b4 = 1 * (1/3)^3 = 1/27 => Sufficient

2) b3 = 1/3
b4 = (1/9) * (1/3) = 1/27 => Sufficient

ANSWER: D

Suruchim12 · Answer

Hi  Bunuel  /  ScottTargetTestPrep  /  KarishmaB

Can you pls help me understand this better. If the question states that M is any positive INTEGER, how can any element in the sequence be a fraction? - which is what we'll get if we have to go by st. 2 and also if we have to just use some numbers for Mth element and (M-1)th element.

Thanks!

KarishmaB · Answer

M is not the actual value in the list. When we say the Mth element, we mean say the 1st element or 2nd element or 3rd element etc. We cannot have a 0th element or 2.1th element and that is why we are given that M must be a positive integer. The actual element in the list can take any fraction or negative value. Given: "when you subtract the Mth element from the (M-1)th element, you get twice the Mth element" Take an example: This means that when we subtract the 2nd element from the 1st element, we get twice the 2nd element. Let's write these terms of the sequence in our standard form, say using t_m as a generic term. When m = 2 We are given that: t_1- t_2 = 2 * t_2 So, t_2 = \frac{t_1}{3} t_3 = \frac{t_2}{3} and so on.. Hence this is a Geometric Progression with common ratio as 1/3. Now when we are given any term, we can find all other terms (because it gives us the first term a) Answer (D) Check out this post on sequences to understand how to deal with them: https://anaprep.com/algebra-introducing-sequences/

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In a certain sequence, when you subtract the Mth element from the (M-1

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