if a1 =5 an an =5an-1 then whats the value of a4

Answer 1

To find the value of a4, we can use the recursive equation given.

Given: a1 = 5, an = 5an-1

First, let's substitute the values of n in the equation to see if a pattern emerges:

a2 = 5a2-1
a3 = 5a3-1

We notice that each term in the sequence is equal to 5 times the previous term. So, we can write the recursive equation as:

an = 5 * an-1

Now, let's find the value of a4:

a4 = 5 * a4-1
= 5a3
= 5 * 5a3-1 (substituting a3 using the recursive equation)
= 5 * 5a2
= 5 * 5 * 5a1
= 5 * 5 * 5 * a1 (a1 = 5)
= 5 * 5 * 5 * 5
= 5^4
= 625

Therefore, the value of a4 is 625.