CBSE NCERT Solutions Chapter 5 Arithmetic Progressions Exercise 5.1 Question 4
4. 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)
Solution (i)
It is not an AP because difference between consecutive terms is not same.
Example:
Solution (ii)
It is an AP because difference between consecutive terms is same.
Common difference (d) =
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
Solution (iii)
It is an AP because difference between consecutive terms is same.
Common difference (d) =
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
Solution (iv)
It is an AP because difference between consecutive terms is constant.
Common difference (d) = 4
Fifth term = 2 + 4 = 6
Sixth term = 6 + 4 = 10
Seventh term = 10 + 4 = 14
Therefore, next three terms are
and
Solution (v)
It is an AP because difference between consecutive terms is constant.
Common difference (d) =
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
Solution (vi)
It is not an AP because difference between consecutive terms is not constant.
Example:
Solution (vii)
It is an AP because difference between consecutive terms is constant.
Common difference (d) =
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
Solution (viii)
It is an AP because difference between consecutive terms is constant.
Common difference (d) = 0
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
Solution (ix)
It is not an AP because difference between consecutive terms is not constant.
Example:
Solution (x)
It is an AP because difference between consecutive terms is constant.
Common difference (d) = a
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
Solution (xi)
It is not an AP because difference between consecutive terms is not constant.
Example:
Solution (xii)
Therefore, sequence is like
It is an AP because difference between consecutive terms is constant.
Common difference (d) =
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
Solution (xiii)
It is not an AP because difference between consecutive terms is not constant.
Example:
Solution (xiv)
It is not an AP because difference between consecutive terms is not constant.
Example:
Solution (xv)
Therefore, sequence is like
It is an AP because difference between consecutive terms is constant.
Common difference (d) =
Fifth term =
Sixth term =
Seventh term =
Therefore, next three terms are
and
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