Chapter 5 · Question 1

What is an arithmetic progression? Find the common difference of $45,43,41,39,\ldots$ .

Answer

An arithmetic progression is a list of numbers in which the difference between consecutive terms is constant. For

45,43,41,39,\ldots

, common difference

d=43-45=-2

.

If the same number is added each time, it is an AP. Here

-2

is added each time.

A sequence

a_1,a_2,a_3,\ldots

is an AP if

a_{n+1}-a_n

is constant. This constant is the common difference

d

. Here

43-45=-2

,

41-43=-2

, and

39-41=-2

, so it is an AP with

d=-2

.

An arithmetic progression is a list of numbers in which the difference between consecutive terms is constant.