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Answer: (i) 2, 4, 8, 16 …
This series is not an A.P.
(ii) 2, 5/2, 3, 7/2 ….
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = 5/2 – 2
=> = 1/2 = 0.5
Therefore, d = 0.5
(iii) -1.2, -3.2, -5.2, -7.2 …
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = -3.2 – (-1.2)
=> = -2
Therefore, d = -2
(iv) -10, – 6, – 2, 2 …
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = -6 – (-10)
=> = 4
Therefore, d = 4
(v) 3, 3 + √2, 3 + 2√2, 3 + 3√2
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = 3+√2 – 3
=> = √2
Therefore, d = √2
(vi) 0.2, 0.22, 0.222, 0.2222 ….
This series is not an A.P.
(vii) 0, – 4, – 8, – 12 …
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = -4 – 0
=> = -4
Therefore, d = -4
(viii) -1/2, -1/2, -1/2, -1/2 ….
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = -1/2 – (-1/2)
=> = 0
Therefore, d = 0
(ix) 1, 3, 9, 27 …
This series is not an A.P.
(x) a, 2a, 3a, 4a …
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = 2a – a
=> = a
Therefore, d = a
(xi) a, a2, a3, a4 …
This is not an A.P. series
(xii) √2, √8, √18, √32 …
This is an A.P. series.
This series can be rearranged as: √2, 2√2, 3√2, 4√2
and hence its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = 2√2 – √2
=> = √2
Therefore, d = √2
(xiii) √3, √6, √9, √12 …
This is not an A.P. series
(xiv) 12, 32, 52, 72 …
This is an A.P. series and its common difference d is:
=> d = an – an-1
=> d = a2 – a1
=> = 32 – 12
=> = 20
Therefore, d = 20
(xv) 12, 52, 72, 73 …
This is not an A.P. series
