If the difference between any two consecutive terms of a series is a constant value, then the series is an A.P
(i) Given, the series is 2, 4, 8, 16, …
Here,
a2−a1=4−2=2
a3−a2=8−4=4a4−a3=16−8=8
Note that the difference between any two consecutive terms of the series is not a constant value.
Hence, the given series is not an AP.
(ii) Given, the series is :
2,52,3,72…
Here,
a2−a1=52−2=12a3−a2=3−52=12a4−a3=72−3=12
Note that the difference between any two consecutive terms of the series is a constant value.
Therefore, d=12 and the given numbers are in A.P.
The next three terms are:
a5=72+12=4a6=4+12=92a7=92+12=5
(iii) −1.2,−3.2,−5.2,−7.2……
Here,
a2−a1=(−3.2)−(−1.2)=−2a3−a2=(−5.2)−(−3.2)=−2a4−a3=(−7.2)−(−5.2)=−2
⇒an+1−an is same for all n.
Therefore, d=-2 and the given numbers are in A.P.
Next three terms are:
a5=−7.2−2=−9.2a6=−9.2−2=−11.2a7=−11.2−2=−13.2