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# Which of the Following Sequences Are Arithmetic Progressions? for Those Which Are Arithmetic Progressions, Find Out the Common Difference. 12, 2, −8, −18, ... - CBSE Class 10 - Mathematics

#### Question

Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.

12, 2, −8, −18, ...

#### Solution

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)

12, 2, −8, −18, ...

Here,

First term (a) = 12

a_1 = 2

a_2 = -8

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

Common difference (d) = a_1 - a = a_2  - a_1

Here

a_1 - a = 2 - 12

= - 10

Also

a_2 - a = -8 - 2

= - 10

Since a_1 - a = a_2 - a_1

Hence, the given sequence is an A.P with the common difference d = -10

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Solution Which of the Following Sequences Are Arithmetic Progressions? for Those Which Are Arithmetic Progressions, Find Out the Common Difference. 12, 2, −8, −18, ... Concept: Arithmetic Progression.
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