Question

Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = –3n − 3

Answer 1

Solution:

Given:

To find the first four terms of the sequence which is defined as

$a_n=-3n-3$

First term: n=1

Thus,

$\begin{gathered} a_1=-3(1)-3 \\ \Rightarrow a_1=-6 \end{gathered}$

second term: n=2

$\begin{gathered} a_2=-3(2)-3 \\ \Rightarrow a_2=-9 \end{gathered}$

third term: n=3

$\begin{gathered} a_3=-3(3)-3 \\ \Rightarrow a_3=-12 \end{gathered}$

fourth term: n = 4

$\begin{gathered} a_4=-3(4)-3 \\ \Rightarrow a_4=-15 \end{gathered}$

Hence, the first four terms of the sequence are

$-6,\text{ -9, -12, -15}$