Question

the following sequence is given in recursive form . what is the value of the third term

Answer 1

Given

The first term of the sequence is given by

$a_{1\text{ =}}-2$

$\begin{gathered} \text{For the other terms n, such that n }\ge\text{ 2} \\ a_n=3a_{n-1}-11\text{ } \end{gathered}$

To get the third term, we will need to follow the following steps:

Step1: Obtain the second term

=> This will be obtaine

$\begin{gathered} a_2=3a_{2-1}-11\text{ } \\ a_2=3a_1-11\text{ } \\ a_2=3\times-2_{}-11\text{ } \\ a_2=-6_{}-11\text{ } \\ a_2=\text{ -1}7 \end{gathered}$

Step 2: Obtain the third term

=>This will be gotten by substituting the value of the second term into the equation

$\begin{gathered} a_n=3a_{n-1}-11\text{ } \\ a_3=3a_{3-1}-11\text{ } \\ a_3=3a_2-11\text{ } \\ a_3=3a_2-11\text{ } \\ a_3=3\times-17_{}-11\text{ } \\ a_3=-51_{}-11 \\ a_3=-62 \end{gathered}$