Question

(iii) 2, 2, 2, 2,….. is an AP. (True/False)

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Answer 1

Answer:

True

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Answer 2

The statement 2 , 2 , 2 , 2 , . . . . are in AP is true

Given :

The progression 2 , 2 , 2 , 2 , . . . . is an AP

To find :

Check true / false the statement

Concept :

A sequence of numbers are said to form an Arithmetic progression if the difference between any two consecutive terms is always the same.

Solution :

Step 1 of 2 :

Write down the given progression

Here the given progression is 2 , 2 , 2 , 2 , . . . .

Step 2 of 2 :

Determine 2 , 2 , 2 , 2 , . . . . is an AP or not

First term = a₁ = 2

Second term = a₂ = 2

Third term = a₃ = 2

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.

Now

a₂ - a₁ = 2 - 2 = 0

a₃ - a₂ = 2 - 2 = 0

So on

Thus we get , a₂ - a₁ = a₃ - a₂

Since the difference between any two consecutive terms is same , which is 0

So the given progression is an arithmetic progression.

Hence the statement 2 , 2 , 2 , 2 , . . . . are in AP is true

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