## 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?

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

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Algebra |

Sub-Topic | Sequences |

Difficulty | Easy – Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__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__

__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__

__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)__

__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.