Question

If a1 =7 and an= 3an-1 + 4 then find the value of a4. a

Answer 1

Using the recurrence relation an= 3an-1 + 4 and the initial condition a1 = 7, the value of a4 is calculated step by step to be 241.

Step-by-step explanation:

To find the value of a4, we use the given recurrence relation an= 3an-1 + 4, with the initial value a1 = 7. Starting with n=2, we can find the subsequent terms up to n=4.

1. For n=2: a2 = 3a1 + 4 = 3(7) + 4 = 21 + 4 = 25.
2. For n=3: a3 = 3a2 + 4 = 3(25) + 4 = 75 + 4 = 79.
3. For n=4: a4 = 3a3 + 4 = 3(79) + 4 = 237 + 4 = 241.

Therefore, the value of a4 is 241.

Answer 2

For this case we know that:

a1= 7

`a_n=3a_(n-1)+4`

Then for a4 we have:

`a_4=3a_3+4=3(3a_2+4)+4=9a_2+16=9(3a_1+4)+16=27a_1+36+16`

And then we can replace and we got:

a4= 27*7 +52= 241