Question

1. Take any Arithmetic Progression.
2. Add a fixed number to each and every term of AP. Write the resulting numbers as a
3. Similarly subtract a fixed number from each and every term of AP. Write the resulting
numbers as a list.
4. Multiply and divide each term of AP by a fixed number and write the resulting numbers
as a list.
5. Check whether the resulting lists are AP in each case.​

Answer 1

Step-by-step explanation:

Ok lets take on the set of even number 2,4,6,8,......

Case 1:Adding a fixed number

Hence taking the fixes number as 1

We add on 1 toe ach of the terms hence

2+1,4+1,6+1,8+1...... =3,5,7,9......

COMMON DIFFERENCE =2

(5-3)=2,(7-5)=2,(9-7)=2

Case2:subtracting 1 from each

We get

2-1,4-1,6-1,8-1.........?=1,3,5,7,........

COMMON DIFFERENCE=2

Case 3:Multiplying a fixed number

Let's take the set of numbers 1,2,3,4

Mulitipying each term with 1=

1*1,2*1,3*1,4*1....=.1,2,3,4....

COMMON DIFFERENCE =1

Case 4:dividing with a fixed number

1/1,2/1,3/14/1....=1,2,3,4....

COMMON DIFFERENCE =1

Now coneing to all cases its clearly visible that in case 1,2,3 and 4 the set of numbers have a common diiferenve and hence firms an Ap