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# In a sequence of numbers in which each term is 2 more than the precedi

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In a sequence of numbers in which each term is 2 more than the precedi  [#permalink]

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26 Apr 2019, 02:09
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In a sequence of numbers in which each term is 2 more than the preceding term, what is the fourth term?

(1) The last term is 90.
(2) The first term is 2.

DS12602.01
OG2020 NEW QUESTION

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Re: In a sequence of numbers in which each term is 2 more than the precedi  [#permalink]

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26 Apr 2019, 04:02
Difference = 2

From S1:

Last term is 90, but no info about first term.
Hence Insufficient.

From S2:

First term = 2
Next term = 2+2 = 4
4th term = 8
Sufficient.

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Re: In a sequence of numbers in which each term is 2 more than the precedi  [#permalink]

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26 Apr 2019, 17:19
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Bunuel wrote:
In a sequence of numbers in which each term is 2 more than the preceding term, what is the fourth term?

(1) The last term is 90.
(2) The first term is 2.

DS12602.01
OG2020 NEW QUESTION

We know that these numbers form an arithmetic sequence with a difference of 2. The original question: $$a_4=?$$

1) If the last term is the 4th term, then $$a_4=90$$. However, if the last term is the 5th term, then $$a_4=90-2=88$$. Thus, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

2) We know that $$a_1=2$$, so $$a_4=2+(4-1)\cdot 2=8$$. Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient

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Re: In a sequence of numbers in which each term is 2 more than the precedi  [#permalink]

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29 Apr 2019, 10:59
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Bunuel wrote:
In a sequence of numbers in which each term is 2 more than the preceding term, what is the fourth term?

(1) The last term is 90.
(2) The first term is 2.

Given: Sequence of numbers is such that each term is 2 more than the preceding term

Target question: What is the value of term_4?

Statement 1: The last term is 90.
We have no idea how many terms there are in the sequence. So, the last term could be term_5 or term_9 or term_12 or . . .

Consider these two possible cases:
Case a: The last term is term_6. In this case, term_6 = 90. term_5 = 88, term_4 = 86, term_3 = 84....etc. So, the answer to the target question is term_4 = 86
Case b: The last term is term_5. In this case, term_5 = 90. term_4 = 88, term_3 = 86 ....etc. So, the answer to the target question is term_4 = 88
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The first term is 2.
If term_1 = 2, then: term_2 = 4, term_3 = 6, term_4 = 8, . .. etc
The answer to the target question is term_4 = 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: In a sequence of numbers in which each term is 2 more than the precedi  [#permalink]

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29 Apr 2019, 16:10
Hi All,

We're told that in a sequence of numbers, each term is 2 more than the preceding term. We're asked for the fourth term. Sequence questions often come down to two pieces of information: the "formula" for how the sequence progresses and one (or more) of the terms (so that you can calculate the other terms in the sequence). The prompt tells us the formula (add 2 as you go from term to term), so we just need one of the terms in the sequence to find the value of the 4th term.

(1) The last term is 90.

With the information in Fact 1, we can 'work backwards' to find the preceding terms (88...86...84...82, etc.), but we don't know which one will be the 4th term.
Fact 1 is INSUFFICIENT

(2) The first term is 2.

With the information in Fact 2, we can 'work forwards' from the 1st term to find the 4th term:
2nd term = 2+2 = 4
3rd term = 4+2 = 6
4th term = 6+2 = 8
Fact 2 is SUFFICIENT

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In a sequence of numbers in which each term is 2 more than the precedi  [#permalink]

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14 May 2019, 06:06

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given
• In a sequence of numbers, each term is 2 more than the preceding term.

We need to determine
• The value of the fourth term.

As each term is 2 more than the preceding term, the series is an example of an arithmetic progression.
Hence, to find the value of the fourth term, we need to know either the 1st term or the value of any other specific term.
With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, the last term is 90.
• However, from this statement we don’t know which term is the last term.
Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, the first term is 2.
As every term is 2 more than the previous term, we can say
• Second term = 2 + 2 = 4
• Third term = 4 + 2 = 6
• Fourth term = 6 + 2 = 8
As we can determine the value of the fourth term, we can say statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 2 individually, this step is not required.
Hence, the correct answer choice is option B.

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In a sequence of numbers in which each term is 2 more than the precedi   [#permalink] 14 May 2019, 06:06
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