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

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

• 19

• 21

• 38

• 42

#### Solution

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

Explanation:

∵ S_n = n/2 [2a + (n - 1)d]

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

798 = 2n + n(n - 1)d  ........(i)

And a_n = 20

⇒ a + (n - 1)d = 20  .....[because a_n = 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

⇒ 978 = 2n

∴ n = 798/21 = 38

Concept: Sum of First n Terms of an A.P.
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#### APPEARS IN

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