Question

For each geometric sequence, write a recusive rule by finding the commom ratio by calculating the ration of consecutive terms. Write an exlicit rule for the sequence by writing each term as the product of the first tern and a power of the common ratio.

n- 1, 2, 3, 4, 5
An- 2, 6, 18, 54, 162

Answer 1

`a_n=2.(3)^(n-1)`

Explanation:

Given sequence is:

2,6,18,54,162

So the common ratio can be found by dividing the second term by first term:

r = 6/2 = 3

The standard formula for geometric sequence is:

`a_n=a_1r^(n-1)`

Putting the value of r

`a_n=2.(3)^(n-1)`

So,

`a_1=2.(3)^(1-1) => 2.3^0 = 2*1 = 2\\a_2=2.(3)^(2-1) => 2.3^1 = 2*3 = 6\\a_3=2.(3)^(3-1) => 2.3^2 = 2*9 = 18\\a_4=2.(3)^(4-1) => 2.3^3 = 2*27 = 54\\a_5=2.(3)^(5-1) => 2.3^4 = 2*81 = 162`