Question

Consider a population that grows according to the recursive ruleLn+1 = Ln + 24,with an initial population Lo = 7.Find the next five terms in the sequence:L1 =L2 =L3 =L4L5 =

Answer 1

Given the recursive rule:

$L_{n+1}=L_n+24$

With an initial population of:

$L_o=7$

Let's determine the next five terms.

Since the first term is 7,

• For the L1, substitute 0 for n and solve:

$\begin{gathered} L_{0+1}=L_0+24 \\ \\ L_1=7+24 \\ \\ L_1=31 \end{gathered}$

• For L2, substitute 1 for n and solve:

$\begin{gathered} L_{1+1}=L_1+24 \\ \\ L_2=31+24 \\ \\ L_2=55 \end{gathered}$

• For L3, substitute 2 for n and solve:

$\begin{gathered} L_{2+1}=L_2+24 \\ \\ L_3=55+24 \\ \\ L_3=79 \end{gathered}$

• For L4, substitute 3 for n and solve:

$\begin{gathered} L_{3+1}=L_3+24 \\ \\ L_4=79+24 \\ \\ L_4=103 \end{gathered}$

• For L5, substitute 4 for n and solve:

$\begin{gathered} L_{4+1}=L_4+24 \\ \\ L_5=103+24 \\ \\ L_5=127 \end{gathered}$

ANSWER:

• L1 = 31

,

• L2 = 55

,

• L3 = 79

,

• L4 = 103

,

• L5 = 127