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OG 2020: Question No. 326

After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

1. The sum of the first 3 terms in the sequence is 6.
2. The fourth term in the sequence is 6.

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Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• In a sequence, after the first two terms, each term is formed by adding all of the preceding terms.

We need to determine

• Whether the fifth term is 12 or not.

If we assume the first term as ‘a’ and second term as ‘b’, then we can say

• Third term = a + b
• Fourth term = a + b + (a + b) = 2(a + b)
• Fifth term = a + b + (a + b) + 2(a + b) = 4(a + b)

Therefore, if 4(a + b) = 12, it means a + b = 3

Hence, to determine whether fifth term is 12 or not, we need to know whether a + b is 3 or not.

With this understanding, let us now analyse the individual statements.

 

Step 3: Analyse Statement 1

As per the information given in statement 1, the sum of the first 3 terms in the sequence is 6.

• Therefore, a + b + (a + b) = 6

Or, 2(a + b) = 6

Or, a + b = 3

As a + b = 3, we can say fifth term is 12.

Hence, statement 1 is sufficient to answer the question.

 

Step 4: Analyse Statement 2

As per the information given in statement 2, the fourth term in the sequence is 6.

• Therefore, 2(a + b) = 6

Or, a + b = 3

As a + b = 3, we can say fifth term is 12.

Hence, statement 2 is sufficient to answer the question.

 

Step 5: Combine Both Statements Together (If Needed)

Since we could determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer is option D.

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