$${n^{th}}$$ Term of an AP

$${n^{th}}$$ Term of an AP

Johan Carl Fredrich Gauss, the father of arithmetic progressions, was asked to find the sum of integers from 1 to 100 without using a counting frame.

This was unheard of, but Gauss, the genius that he was, took up the challenge.

He listed the first 50 integers, and wrote the subsequent 50 in reverse order below the first set.

To his surprise, the sums of the numbers next to each other was 101 i.e. 100 + 1, 99 + 2, 51 + 50, etc.

He found there were 50 such pairs and ended up multiplying 101 with 50 to give an output 5050

Does this confuse you like it has confused Jack? Lesson Plan

 1 What Is Meant by Arithmetic Progression? 2 Important Notes on Nth term of Arithmetic Progression 3 Tips and Tricks 4 Solved Examples on Nth term of Arithmetic Progression 5 Interactive Questions on Nth term of Arithmetic Progression

What Is Meant by Arithmetic Progression?

Arithmetic progression can be defined as a sequence where the differences between every two consecutive terms are the same.

Consider the following AP:

2, 5, 8, 11, 14

The first term a of this AP is 2, the second term is 5, the third term is 8, and so on. We write this as follows:

T1 = a = 2

T2 = 5

T3 = 8

The nth term of this AP will be denoted by Tn.

For example, what will be the value of the following terms?

T20, T45, T90, T200

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus