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https://www.youtube.com/watch?v=5o2Idkx88Yw
Watch this video to understand an example of Arithmetic Progression- Sequence and Series Part 1.
SEQUENCE AND SERIES - PART 1
ARITHMETIC PROGRESSION
A progression is a special type of sequence for which it is possible to obtain a formula for the nth term.
The Arithmetic Progression is the most commonly-used sequence in Mathematics.
A mathematical sequence in which the difference between two consecutive terms is always a constant is said to be Arithmetic Progression and is abbreviated as AP.
In AP, we will come across three main terms, which are denoted as:
Common difference (d)
nth Term (an)
Sum of the first n terms (Sn)
Common Difference in Arithmetic Progression
In this progression, for a given series, the terms used are the first term, the common difference between the two terms, and the nth term. Suppose, a1, a2, a3, ……………., an is an AP, then; the common difference “ d ” can be obtained as;
d = a2 – a1 = a3 – a2 = ……. = an – an – 1
Where “d” is a common difference. It can be positive, negative or zero.
First Term of AP
The AP can also be written in terms of common difference, as follows;
a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d
where “a” is the first term of the progression.
nth term of an AP
The formula for finding the n-th term of an AP is:
an = a + (n − 1) × d
Sum of N Terms of AP
Consider an AP consisting of “n” terms.
\(S = \frac{n}{2}[2a + (n − 1) × d]\)
Sum of AP when the Last Term is Given
\(S = \frac{n}{2}\) (first term + last term)
Watch this video to understand an example of Arithmetic Progression- Sequence and Series Part 1.
SEQUENCE AND SERIES - PART 1
ARITHMETIC PROGRESSION
A progression is a special type of sequence for which it is possible to obtain a formula for the nth term.
The Arithmetic Progression is the most commonly-used sequence in Mathematics.
A mathematical sequence in which the difference between two consecutive terms is always a constant is said to be Arithmetic Progression and is abbreviated as AP.
In AP, we will come across three main terms, which are denoted as:
Common difference (d)
nth Term (an)
Sum of the first n terms (Sn)
Common Difference in Arithmetic Progression
In this progression, for a given series, the terms used are the first term, the common difference between the two terms, and the nth term. Suppose, a1, a2, a3, ……………., an is an AP, then; the common difference “ d ” can be obtained as;
d = a2 – a1 = a3 – a2 = ……. = an – an – 1
Where “d” is a common difference. It can be positive, negative or zero.
First Term of AP
The AP can also be written in terms of common difference, as follows;
a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d
where “a” is the first term of the progression.
nth term of an AP
The formula for finding the n-th term of an AP is:
an = a + (n − 1) × d
Sum of N Terms of AP
Consider an AP consisting of “n” terms.
\(S = \frac{n}{2}[2a + (n − 1) × d]\)
Sum of AP when the Last Term is Given
\(S = \frac{n}{2}\) (first term + last term)
05 Jan 2026, 07:24
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