Question

Write the explicit formula for the sequences
3,9,27,81,...

Answer 1

Explanation:

This is a geometric sequence. The general formula for any term is

t_n = a*r^(n-1)

t1 = 3

r = 3

t_n = 3* 3^(n - 1)

t_4 should be 81

t_4 = 3*3^(n - 1)

t_4 = 3*3^3

t_4 = 3 * 27

t_4 = 81

Answer 2

an = 3 * (3)^ (n-1) or

an = 3^n

Explanation:

To find the common ratio, take the second term and divide by the first term

9/3 = 3

To verify take the third term and divide by the second

27/9 =3

Since this is a geometric sequence, it is of the form

an = a1*r^(n-1) where a1 is the first term and r is the common ration

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

Since the first term is the same as the term inside the parentheses, we can combine

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

= 3^ (1+n-1)

= 3^ (n)