two terms of an arithmetic sequence are 15 and 45. Create three different arithmetic sequences given these terms
They do not have to be consective terms.
0,15,30,45,60,... would be one
1,2,3,4...15,16,...44,45,... (all consecutive integers) would be another
Surely you can think of another.
To create three different arithmetic sequences given the terms 15 and 45, we need to find the common difference first.
The common difference in an arithmetic sequence is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term.
Common difference = 45 - 15 = 30
Now that we have the common difference, we can create three different arithmetic sequences:
Sequence 1:
Starting with the first term 15, we can simply add the common difference repeatedly to generate the next terms.
The terms would be: 15, 45, 75, 105, ...
Sequence 2:
Similarly, starting with the second term 45, we can also add the common difference to generate the next terms.
The terms would be: 45, 75, 105, 135, ...
Sequence 3:
We can also create a sequence by subtracting the common difference from the first term.
The terms would be: 15, -15, -45, -75, ...
These are three different arithmetic sequences that can be generated using the given terms 15 and 45.