Neco 2024 Mathematics Question 9

Practice essay / theory question 9 from the 2024 Neco Mathematics examination. This question covers Sequences and Series .

Neco 2024 Mathematics Essay / Theory

Topic: Sequences and Series

Question 9 NECO • 2024 • MATHEMATICS • essay

A certain sequence is defined as follows: the first term is 3. The second term is obtained by adding 4 to the first term. From the third term onward, each term is the sum of the two preceding terms.

Question Parts

( a )

Write the first six terms of the sequence.

( b )

Prove that for \(n \ge 3\), the \(n^{th}\) term can be expressed as \(a_n = 3F_{n-2} + 4F_{n-1}\), where \(F_k\) denotes the \(k^{th}\) term of the standard Fibonacci sequence (\(F_1 = 1, F_2 = 1\)).

( c )

Using the result in part (b), find the sum of the first ten terms of the sequence.

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About This Question

This is Neco 2024 Mathematics Question 9. It is one of the essay questions from the 2024 Neco Mathematics examination.

The question covers Sequences and Series .

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