What is the recursive formula for 2, 6, 18, 54, 162, ...

Question

I need to find the recursive formula for 2, 6, 18, 54, 162, ...

Answer 1

6 = 3x2

an = 3an-1 = 3 times the previous term

nth term = 3 times the n-1st term

2, 6, 18, 54, ...

a1 = 2

a2 = 3a1

a3 = 3a2

a4 =3a3

a4 =3(3)(3)2 = 2(3^(n-1)) = an

an = 2(3^(n-1))

Answer 2

A recursive formula is a formula that defines any term of a sequence in terms of its preceding term (s).

Notice: these terms are rapidly increasing. In fact, this is a geometric sequence with a common ratio, r, of 3. Each termi 3 times as large as the previous term.

The recursive formula of a geometric sequence is:

a₁ = 2

a_n = 3a_{n-1 ... for n > 1}

Answer 3

Each succesive term is three times the previous.

a_n+1 = 3a_n