# Which of the Following Sequences Are Arithmetic Progressions? for Those Which Are Arithmetic Progressions, Find Out the Common Difference. P, P + 90, P + 180 P + 270, ... Where P = (999)999 - Mathematics

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

p, p + 90, p + 180 p + 270, ... where p = (999)999

#### 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)

p, p + 90, p + 180 p + 270, ... where p = (999)999

Here

First term (a) = p

a_1 = p + 90

a_2 = p + 180

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= p + 90 - p

= 90

Also

a_2 - a_1 = p + 180 - p - 90

= 90

Since a_1 - a = a_2 - a_1

Hence, the given sequence is an A.P and its common difference is d = 90

Concept: Arithmetic Progression
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.3 | Q 6.06 | Page 11