# Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. 3, 3 +√2, 3 + 2√2, 3 + 3√2 - Mathematics

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. 3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2

#### Solution

3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2

Here,

a2 - a1 = 3 + sqrt2 - 3 = sqrt2

a3 - a2 = (3 + 2sqrt2) - (3 + sqrt2) = sqrt2

a4 - a3 = (3 + 3sqrt2) - (3 + 2sqrt2) = sqrt2

⇒ an+1 - an is same every time.

Therefore, d = sqrt2 and the given numbers are in A.P.

Three more terms are

a5 = (3 + sqrt2) + sqrt2 = 3 + 4sqrt2

a6 = (3 + 4sqrt2) + sqrt2 = 3 + 5sqrt2

a7 = (3 + 5sqrt2) + sqrt2 = 3 + 6sqrt2

Concept: Arithmetic Progression
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.1 | Q 4.05 | Page 99