a) divide the previous term by 2
b) add 7 to previous term to get next term
Step-by-step explanation:
a) {40,20,10,5....}
common difference deals with subtraction of terms
common ratio deals with division of terms
So we could try each one to determine what pattern the sequence follows:
To determine the next term in an arithmetic sequence, we need to find the difference between two terms
common difference = 2nd term - 1st term = 3rd term - 2nd term
1st term = 40, 2nd term = 20
common difference = 20 - 40 = 10 -20 = 5 -10
common difference = -20 = -10 = -5
From the above the common difference is different. So we use geometric sequence
For geometric sequence:
common ratio = 2nd term/1st term =3rd term/ 2nd term
common ratio = 20/40 = 10/20
= 1/2 = 1/2
Since the common ratio is the same, it is a geometric sequence
1st term = 40. $0 is the previos term of 20.
So if we are to find the next term which is 20, we would divide the previous term by 2.
This becomes 40/2 = 20 (this is the next term after 40 in the sequence)
To get the next term after 20, we divide the previuos term which is 20 by 2.
This becomes 20/2 = 10
We follow this step for the next term after 10.
As a result for this sequence, to get the next term, we divide the previous term by 2
So we would match this sequence with divide the previous term by 2
b) {4, 11, 18, 25,...}
common difference = 2nd term - 1st term = 3rd term - 2nd term
common difference = 11 - 4 = 18 - 11 = 25 - 18
common differnce = 7 = 7 = 7
The common difference is the same
From the above, we add 7 to previous term to get next term
So we would match {4, 11, 18, 25,...} to add 7 to previous term to get next term