In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is

The correct option is D - 47.

[as per provisional answerkey]

Solution

The question describes a Fibonacci-style sequence where each term (starting from the third) is the sum of the two preceding terms. We are given the first two terms and need to find the sixth term.

Let the sequence be represented as T₁, T₂, T₃, T₄, T₅, T₆.

• First term (T₁): 4 (Given)
• Second term (T₂): 7 (Given)
• Third term (T₃): T₁ + T₂ = $4+7=11$
• Fourth term (T₄): T₂ + T₃ = $7+11=18$
• Fifth term (T₅): T₃ + T₄ = $11+18=29$
• Sixth term (T₆): T₄ + T₅ = $18+29=47$

The sixth number in the sequence is 47.

Why the other options are incorrect

• Option (a) - 29: This is the 5th term of the sequence, not the 6th.
• Option (b) - 37: This value does not follow the additive rule of the sequence; it is likely a calculation error.
• Option (c) - 43: This value is incorrect; it may result from a miscalculation in adding the 4th and 5th terms $(18+29)$.

Key Concept

Recursive sequences where each term is defined as the sum of the preceding terms (T_n = T_n-1 + T_n-2).