Question

formulas in arithmetic progression​

Answer 1

Answer:

Formula Lists

General Form of AP a, a + d, a + 2d, a + 3d, . . .

The nth term of AP an = a + (n – 1) × d

Sum of n terms in AP S = n/2[2a + (n − 1) × d]

Sum of all terms in a finite AP with the last term as 'l' n/2(a + l)

Answer 2

Answer:

Here is your answer

Step-by-step explanation:

There are two major formulas we come across when we learn about Arithmetic Progression, which is related to:

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

Example: Find the nth term of AP: 1, 2, 3, 4, 5…., an, if the number of terms are 15.

Solution: Given, AP: 1, 2, 3, 4, 5…., an

n=15

By the formula we know, an = a+(n-1)d

First-term, a =1

Common difference, d=2-1 =1

Therefore, an = 1+(15-1)1 = 1+14 = 15

Note: The finite portion of an AP is known as finite AP and therefore the sum of finite AP is known as arithmetic series. The behaviour of the sequence depends on the value of a common difference.

If the value of “d” is positive, then the member terms will grow towards positive infinity

If the value of “d” is negative, then the member terms grow towards negative infinity.

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