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In an AP if a = 1, an = 20 and Sn = 399, then n is ______.

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Question

In an AP if a = 1, an = 20 and Sn = 399, then n is ______.

Options

  • 19

  • 21

  • 38

  • 42

MCQ
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Solution

In an AP if a = 1, an = 20 and Sn = 399, then n is 38.

Explanation:

∵ Sn = `n/2[2a + (n - 1)d]`

339 = `n/2[2 xx 1 + (n - 1)d]`

798 = 2n + n(n – 1)d  ...(i)

And an = 20

⇒ a + (n – 1)d = 20  ...[∵ an = a + (n – 1)d]

⇒ 1 + (n – 1)d = 20

⇒ (n – 1)d = 19  ...(ii)

Using equation (ii) in equation (i), we get

798 = 2n + 19n

⇒ 798 = 21n

∴ n = `798/21` = 38

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Chapter 5: Arithematic Progressions - Exercise 5.1 [Page 47]

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NCERT Exemplar Mathematics Exemplar [English] Class 10
Chapter 5 Arithematic Progressions
Exercise 5.1 | Q 17 | Page 47

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