which of the following are APs? if they form an AP,find the commom difference d and write three more terms:1:-a,2a,3a,4a....
Answers
Answer:
Answer
a,b,c are said to be in AP if the common difference between any two consecutive number of the series is same ie b−a=c−b⇒2b=a+c
(i) It is not in AP, as the difference between consecutive terms is different.
(ii) It is in AP with common difference d=
2
5
−2=
2
1
,
t
n
=a+(n−1)d
a=2
t
5
=2+(5−1)
2
1
Next three terms are 4,
2
9
,5
(iii) It is in AP with common difference d=−3.2+1.2=−2 ,and a=−1.2
Next three terms are
a+(5−1)d=−9.2,
a+(6−1)d=−11.2,
a+(7−1)d=−13.2
(iv) It is in AP with common difference d=−6+10=4, and
a=−10
Next three terms are
a+(5−1)d=6,
a+(6−1)d=10,
a+(7−1)d=14
(v) It is in AP with common difference d=3+
2
−3=
2
, and
a=3
Next three terms are
a+(5−1)d=3+4
2
,
a+(6−1)d=3+5
2
,
a+(7−1)d=3+6
2
(vi) It is not in AP since 0.22−0.2
=0.222−0.22
(vii) It is in AP with common difference d=−4−0=−4 and a=0,
Next three terms are
a+(5−1)d=−16,
a+(6−1)d=−20,
a+(7−1)d=−24
(viii) It is in AP, with common difference 0, therefore next three terms will also be same as previous ones, i.e., −
2
1
(ix) It is not in AP since 3−1
=9−3
(x) It is in AP with common difference d=2a−a=a and first term is a,
Next three terms are
a+(5−1)d=5a,
a+(6−1)d=6a,
a+(7−1)d=7a
(xi) It is not in AP, as the difference is not constant.
(xii) It is in AP with common difference d=
2
and a=
2
,
Next three terms are
a+(5−1)d=5
2
=
50
,
a+(6−1)d=
72
,
a+(7−1)d=
98
(xiii) It is not in AP as difference is not constant.
(xiv) It is not in AP as difference is not constant.
(xv) It is in AP with common difference d=5
2
−1=24 and a=1,
Next three terms are
a+(5−1)d=97,
a+(6−1)d=121,
a+(7−1)d=145