CBSE Class 10-Mathematics: Chapter – 5 Arithmetic Progressions Part 27 (For CBSE, ICSE, IAS, NET, NRA 2022)
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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