The second term of the arithmetic progression (an) is 4, and its ninth term is 13. Find the difference of this progression.

| January 11, 2021 | education

Let’s use the formula by which we will find the term of the progression. This formula is shown at the very top in the screenshot. Although we are given the second and ninth terms of the progression, to find out the difference, we need to find the first term of the progression first. We will find the first term through the difference unknown to us so far, but knowing the values ​​of the second and ninth terms, we bring the equations to the form d = 4-a1 and 8d = 13-a1. That is, you can see that if you multiply the first equation by 8, then both equations will be equal to each other. We simplify them and do not touch the difference in progression yet. We get that the first term of the progression is 19/7. And already the difference of the progression can be calculated by the formula d = 4-a1. By subtracting the fractions, we get the difference 9/7.
The answer is 9/7.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.