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Arithmetic Progressions

Answer:

In the given problem, we are given various sequences.

We need to find out that the given sequences are an A.P or not and then find its common difference (d)

(i) 

Here,

First term (a) = 3

Now, for the given to sequence to be an A.P,

Common difference (d

Here,

Also,

Since 

Hence, the given sequence is not an A.P

(ii) 

Here,

First term (a) = 0

Now, for the given sequence to be an A.P,

Common difference (d

Here

Also,

Since 

Hence, the given sequence is an A.P and its common difference is 

(iii) 

Here,

First term (a) = 

Now, for the given to sequence to be an A.P,

Common difference (d

Here,

Also,

Since 

Hence, the given sequence is not an A.P

(iv) 

Here,

First term (a) = 12

Now, for the given to sequence to be an A.P,

Common difference (d

Here,

Also,

Since …

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