Learn Class 10 Math - Arithmetic Progressions

The word arithmetic progression is a series of terms in which the numbers are present in the order sequence. And the difference between the consecutive numbers always remains constant. This sequence is also known as Arithmetic progression.

Example:

• Natural number series include the numbers from 1, 2, 3, 4, 5, ….so on.
• The difference between the two consecutive numbers is the same, i.e., 1
• The difference between any even number and an odd number always remains the same.

Types of Arithmetic Progression

When we see the types, then they are three different types. The types are discussed below:

• Geometric progression
• Harmonic progression
• Arithmetic progression

Sum of Arithmetic Progression

The formulas of an arithmetic progression are given below:

• AP nth term.
• And their sum,i.e., the sum of n terms.

Question 1:

Evaluate n, when a = 10, d = 5, an = 95.

Answer:

It is given that a = 10, d = 5, & an = 95

With the help of the formula, we see that.

an = a + (n − 1) (d)

95 = 10 + (n − 1) (5)

(n − 1) (5) = 95 – 10 = 85

(n − 1) = 85/ 5

(n − 1) = 17

n = 1 + 17

n = 18

With the help of this formula, we will get the value n. And the value of n is equal to 18.