Which of the following form an AP? Justify your answer. (i) –1, –1, –1, –1, ... (ii) 0, 2, 0, 2, ... (iii) 1, 1, 2, 2, 3, 3,... (iv) 11, 22, 33,... (v) 1 2 , 1 3 , 1 4 , ... (vi) 2, 22, 23, 24 , ... (vii) 3 , 12 , 27 , 48 , ...
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(I), (ii), (IV), (V) is an AP
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1 and 4
Compare the given series with a
1
,a
2
,a
3
......, we get
a
2
−a
1
=1−1=0
a
3
−a
2
=1−1=0
a
4
−a
3
=1−1=0
This shows that the difference of a term and preceding term is always same.
Hence, the given sequence forms an A.P.
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