Grade 12 Questions on Sequences and Series

Question 1

A quadratic pattern is given by \(\; T_{n} = n^{2} + bn + c\). Find the values of \(b\) and \(c\) if the sequence starts with the following terms:

$-1 \; ; \; 2 \; ; \; 7 \; ; \; 14 \; ; \; \ldots$

Question 2

The terms \(p; (2p+2); (5p+3)\) form an arithmetic sequence. Find \(p\) and the \(15^{\text{th}}\) term of the sequence.

Question 3

The second term of an arithmetic sequence is \(-\text{4}\) and the sum of the first six terms of the series is \(\text{21}\).

  1. Find the first term and the common difference.
  2. Hence determine \(T_{100}\).

Question 4

Consider the following geometric sequence: \(\enspace y + 5\enspace ; \enspace y + \frac{50}{3}\enspace ; \enspace y + \frac{10}{9}\)

Find \(y\).

Question 5

Given the geometric sequence: \(6+p ; 10+p ; 15+p\)

  1. Determine \(p\), (\(p \ne -\text{6} \text{ or } -\text{10}\)).
  2. Show that the constant ratio is \(\frac{5}{4}\).
  3. Determine the tenth term of this sequence correct to one decimal place.

Question 6

The second and fourth terms of a convergent geometric series are 36 and 16 , respectively. Find the sum to infinity of this series, if all its terms are positive.

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