Question

How do you write an explicit formula for this sequence: 3, 6, 12, 24?

Answer 1

`3 . 2^(n-1)`

Explanation:

This is a geometric sequence , the standard sequence being :

`a , ar , ar^2 , ar^3 , .................... , ar^(n-1)`

where a , is the 1st term and r , the common ratio

here a = 3 and `r = 6/3 = 12/6 = 24/12 = 2`

to generate terms in the sequence use `ar^(n-1)`

`rArr ar^(n-1) = 3.2^(n-1)`

so 1st term n = 1 : `3.2^(1-1) = 3.2^0 = 3.1 = 3`

2nd term n= 2 : `3.2^(2-1) = 3.2^1 = 6`

4th term n=4 : `3.2^(4-1) = 3.2^3 = 3.8 = 24`