Question

question
if $a_1 = 10$ and $a_{n+1} = 5a_n + 4$ then find the value of $a_5$.

Explanation:

Step1: Find \(a_2\)

Given \(a_1 = 10\) and the recurrence relation \(a_{n + 1}=5a_n + 4\). For \(n = 1\), we substitute \(a_1\) into the formula:
\(a_2=5a_1 + 4=5\times10 + 4 = 50+4=54\)

Step2: Find \(a_3\)

Now, use \(a_2 = 54\) to find \(a_3\). For \(n = 2\):
\(a_3=5a_2 + 4=5\times54+4=270 + 4 = 274\)

Step3: Find \(a_4\)

Use \(a_3 = 274\) to find \(a_4\). For \(n=3\):
\(a_4=5a_3 + 4=5\times274+4=1370 + 4=1374\)

Step4: Find \(a_5\)

Use \(a_4 = 1374\) to find \(a_5\). For \(n = 4\):
\(a_5=5a_4+4=5\times1374 + 4=6870+4=6874\)

Answer:

\(6874\)