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# Which of the Following Sequences Are Arithmetic Progressions? for Those Which Are Arithmetic Progressions, Find Out the Common Difference. 10, 10 + 25, 10 + 26, 10 + 27,... - CBSE Class 10 - Mathematics

#### Question

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

10, 10 + 25, 10 + 26, 10 + 27,...

#### 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)

10, 10 + 25, 10 + 26, 10 + 27,...

Here

First term (a) = 10

a_1 = 10 + 2^5

a_2 = 10 + 2^6

a_3 = 10 + 2^7

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

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

Here

a_2 - a_1 = 10 + 2^6 - 10 - 2^5

= 64 - 32

= 32

Also

a_3 - a_2 = 10 + 2^7 - 10 - 2^6

= 128 - 64

= 64

Since a_1 - a != a_2 - a_1

Hence, the given sequence is not an A.P

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Solution Which of the Following Sequences Are Arithmetic Progressions? for Those Which Are Arithmetic Progressions, Find Out the Common Difference. 10, 10 + 25, 10 + 26, 10 + 27,... Concept: Arithmetic Progression.
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