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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

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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`

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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
  Is there an error in this question or solution?

APPEARS IN

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