Neco 2018 Mathematics Question 9

Practice essay / theory question 9 from the 2018 Neco Mathematics examination. This question covers Sequences and Series .

Neco 2018 Mathematics Essay / Theory

Topic: Sequences and Series

Question 9 NECO • 2018 • MATHEMATICS • essay

A sequence \(\{a_n\}\) is defined by \(a_1 = 2\) and for every integer \(n \ge 1\) the recurrence relation \(a_{n+1}=3a_n+2\) holds.

( a )

Find the value of \(a_4\).

( b )

Prove, by mathematical induction, that for all positive integers \(n\), \(a_n = 3^{,n}-1\).

( c )

Using the formula obtained in part (b), find the sum of the first five terms \(S_5 = a_1+a_2+\dots +a_5\).

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This is Neco 2018 Mathematics Question 9. It is one of the essay questions from the 2018 Neco Mathematics examination.

The question covers Sequences and Series .

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