The 3rd term and 7th terms of an arithmetic progression are 6 and 30 respectively

Determine the :
common difference
First term
10th term.

Hi there!

The key feature of an arithmetic progression is that the change between each term is the same. Let's first calculate this amount of change, known as the common difference.

We can see that there are 4 terms between the values of 6 and 30, as 7 - 3 = 4. By subtracting 6 from 30, and getting 24, we then see that when 4 terms pass, 24 passes. Dividing 24 into 4 equal pieces gets us 6 for each term. Thus, this means that the common difference is 6.

Now, we can calculate the first and 10th term based off this. We know the 3rd term is 6. The first term is 2 terms behind this. With a common difference of 6, this means that the first term is 12 behind 6, or -6.

For the 10th term, we know the 7th term is 30. We know the 10th term is 3 terms after the 7th term. With a common difference of 6, this means the 10th term is 18 after 30, or 48.

Thus, this means the common difference is 6, the first term is -6, and the tenth term is 48.

Hope this helps! Feel free to let me know if you have any additional questions about this specific problem.