Question

What is arthmetic progression? To find the sum of n terms of an arthmetic progression

Answer 1

hey here is your answer ;-


◼Arithmetic progression◼ ;-

✨a succession of number is said to be an arithmetic progression is the difference between any term and the term preceding it is constant throughout this constant is called the common difference of the AP .

✨in other words a succession of number is said to be an arithmetic progression if each term of the sequence can be obtained by adding a fix number to the preceding term accept the first term.

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to find n term :-

✨a+(n-1)d formula is used

hope it helps u....

Answer 2

Arithmetic progression

Definition 1: A mathematical sequence in which the difference between two consecutive terms is always a constant and it is abbreviated as AP.

Definition 2: An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.

Definition 3: The fixed number that must be added to any term of an AP to get the next term is known as the common difference of the AP. Now, let us consider the sequence, 1, 4, 7, 10, 13, 16,… is considered as an arithmetic sequence with common difference 3.

The nth term of AP

Sum of the first n terms

Let us learn here both the formulas with examples.

nth Term of an AP

The formula for finding the n-th term of an AP is:

an = a + (n − 1) × d

Where

a = First term

d = Common difference

n = number of terms

an = nth term

Sum of N Terms of AP

For any progression, the sum of n terms can be easily calculated. For an AP, the sum of the first n terms can be calculated if the first term and the total terms are known. The formula for the arithmetic progression sum is explained below:

Consider an AP consisting “n” terms.

S = n/2[2a + (n − 1) × d]

This is the AP sum formula to find the sum of n terms in series

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