CBSE Class 10-Mathematics: Chapter –5 Arithmetic Progressions Part 27

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Question 26:

Which of the following are APs? If they form an AP, find the common difference d and write three more terms.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi)

(xii)

(xiii)

(xiv)

(xv)

Answer:

(i)

It is not an AP because difference between consecutive terms is not equal.

As

(ii)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term Sixth term

Seventh term

Therefore, next three terms are and .

(iii)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term

Sixth term

Seventh term

Therefore, next three terms are

(iv)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term

Sixth term

Seventh term

Therefore, next three terms are and

(v)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term

Sixth term

Seventh term

Therefore, next three terms are

(vi)

It is not an AP because difference between consecutive terms is not equal.

(vii)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term Sixth term

Seventh term

Therefore, next three terms are and

(viii)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term Sixth term

Seventh term

Therefore, next three terms are

(ix)

It is not an AP because difference between consecutive terms is not equal.

(x)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term

Sixth term

Seventh term

Therefore, next three terms are and

(xi)

It is not an AP because difference between consecutive terms is not equal.

(xii)

Common difference

Fifth term

Seventh term

Therefore, next three terms are

(xiii)

It is not an AP because difference between consecutive terms is not equal.

(xiv)

It is not an AP because difference between consecutive terms is not equal.

(xv)

It is an AP because difference between consecutive terms is equal.

Common difference

Fifth term

Sixth term

Seventh term

Therefore, next three terms are and