Calculate the value of a specific term and the total sum of an arithmetic progression. An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.
Value of the nth Term (aβ):
19
Sum of the First n Terms (Sβ):
100
These results show that for the given first term and common difference, the @n_position-th element in the sequence is @nth_term. Additionally, if you were to add all terms from the start up to this position, the total would be @sum_n.
An arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is constant. This constant is known as the common difference (d). The formula for finding the nth term (aβ) of an arithmetic sequence is: aβ = aβ + (n - 1)d, where aβ is the first term and n represents the position of the term in the sequence.
aβ = aβ + (n - 1)d
The sum of the first n terms of an arithmetic sequence, called an arithmetic series, can be calculated using the formula: Sβ = (n/2)(aβ + aβ).
Sβ = (n/2)(aβ + aβ)
Consider a sequence starting at 5 with a common difference of 3. We want to find the value of the 10th term and the sum of the sequence up to that point.
What is a common difference?The common difference is the constant value that is added to each term to get the subsequent term in an arithmetic sequence. It can be found by subtracting any term from the term that follows it.
Can the common difference be negative?Yes, the common difference can be negative. If the difference is negative, the terms in the sequence will decrease in value as you progress.
What is the difference between a sequence and a series?A sequence is an ordered list of numbers, while a series is the sum of the elements of that sequence.
Β© 2026 Hreflabs LLC. All rights reserved.
Made with β€οΈ for everyone who loves accurate calculations
