# 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.