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Question

Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
(i) 2,4,8,16,....
(ii) 2,52,3,72,...
(iii) 1.2,3.2,5.2,7.2,...
(iv) 10,6,2,2,...
(v) 3,3+2,3+22,3+32
(vi) 0.2,0.22,0.222,0.2222,....
(vii) 0,4,8,12,...
(viii) 12,12,12,12,...
(ix) 1,3,9,27
(x) a,2a,3a,4a,...
(xi) a,a2,a3,a4,...
(xii) 2,8,18,32,...
(xiii) 3,6,9,12,...
(xiv) 12,32,52,72,..
(xv) 12,52,72,73,..

Solution
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a,b,c are said to be in AP if the common difference between any two consecutive number of the series is same ie ba=cb2b=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=522=12,
tn=a+(n1)d
a=2
t5=2+(51)12
Next three terms are 4,92,5

(iii) It is in AP with common difference d=3.2+1.2=2 ,and a=1.2
Next three terms are
a+(51)d=9.2,
a+(61)d=11.2,
a+(71)d=13.2
(iv) It is in AP with common difference d=6+10=4, and
a=10
Next three terms are
a+(51)d=6,
a+(61)d=10,
a+(71)d=14
(v) It is in AP with common difference d=3+23=2, and
a=3
Next three terms are
a+(51)d=3+42,
a+(61)d=3+52,
a+(71)d=3+62
(vi) It is not in AP since 0.220.20.2220.22
(vii) It is in AP with common difference d=40=4 and a=0,
Next three terms are
a+(51)d=16,
a+(61)d=20,
a+(71)d=24
(viii) It is in AP, with common difference 0, therefore next three terms will also be same as previous ones, i.e., 12
(ix) It is not in AP since 3193
(x) It is in AP with common difference d=2aa=a and first term is a,
Next three terms are
a+(51)d=5a,
a+(61)d=6a,
a+(71)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+(51)d=52=50,
a+(61)d=72,
a+(71)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=521=24 and a=1,
Next three terms are
a+(51)d=97,
a+(61)d=121,
a+(71)d=145

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Q1
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
(i) 2,4,8,16,....
(ii) 2,52,3,72,...
(iii) 1.2,3.2,5.2,7.2,...
(iv) 10,6,2,2,...
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(xv) 12,52,72,73,..
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Q2

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