Question

Write the explicit formula

Answer 1

Explanation:

Since there is no single number we can add to one number in the sequence to get to the next one, this is not arithmetic. That means it's geometric, if it's a sequence at all. To get from 2 to 6 we multiply by 3. To get from 6 to 18 we multiply by 3. To get from 18 to 54 we multiply by 3. Therefore, this is in fact geometric and the common ratio is 3. The standard form of a geometric explicit formula is

`A_n=a_1(r)^{n-1` where n is the position of a number in the sequence, a1 is the first number in the sequence, and r is the common ratio. We have then

a1 = 2 and r = 3. Therefore, the explicit formula is

`A_n=2(3)^{n-1` and you can use this to find the value of any number in the sequence. Very handy; much more so than the recursive formula, which requires that all the numbers in a sequence be found in order in order to get to a desired value.