Hello osirvics. Welcome to PF !osirvics said:Homework Statement
The first term of an a.p is -8, the ratio of the 7th term to the 9th term is 5:8. what is the common difference of the progression?
Homework Equations
The Attempt at a Solution
I've tried... it confuses me. Can anyone give me some hints or tips...?
An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference, and it can be positive, negative, or zero.
To find the common difference in an arithmetic progression, you subtract any term in the sequence from its preceding term. This difference will be constant throughout the sequence.
The formula for the nth term in an arithmetic progression is: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
The sum of an arithmetic progression can be found using the formula: Sn = (n/2)(a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.
Arithmetic progressions are used in various real-life scenarios, such as calculating interest rates, predicting population growth, and determining depreciation of assets. They are also used in computer programming and data analysis, where a series of numbers needs to be generated or analyzed.