Find a explicit formula for the recursion a 1 = 3 a n = 5...

Quessyrutty6w

Quessyrutty6w

Answered

2022-07-15

Find a explicit formula for the recursion
a 1 = 3 a n = 5 a n 1 + 12
So i found
a 1 = 3 a 2 = 27 a 3 = 147 a 4 = 747

Answer & Explanation

Monica Dennis

Monica Dennis

Expert

2022-07-16Added 13 answers

Step 1
Try for characteristic equation:
a n = 5 a n 1 + 12 r = 5 a n = c 1 r n + c 2 a n = c 1 ( 5 ) n + c 2
Step 2
apply now a 1 = 3 , a 2 = 27 to find c 1 , c 2
a 1 = 3 = c 1 5 + c 2 a 2 = 27 = c 1 25 + c 2 a n = 6 5 ( 5 ) n 3 a n = 6 ( 5 ) n 1 3
owsicag7

owsicag7

Expert

2022-07-17Added 2 answers

Step 1
If substitute a n 2 , a n 3 , and so on, we have:
a n = 5 k a n k + 12 i = 0 k 1 5 i
a n = 5 k a n k + 12 5 k 1 5 1
a n = 5 k a n k + 3 ( 5 k 1 )
Step 2
Let: k = n 1, then n k = 1
a n = 5 n 1 a 1 + 3 ( 5 n 1 1 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?