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In an AP: Given a = 2, d = 8, Sn = 90, find n and an. - Mathematics

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In an AP:

Given a = 2, d = 8, Sn = 90, find and an.

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Solution

Given that, a = 2, d = 8, Sn = 90
As Sn = n/2 [2a + (n - 1)d]
90 = n/2 [2a + (n - 1)d]
⇒ 180 = n(4 + 8n - 8) = n(8n - 4) = 8n2- 4n
⇒ 8n2 - 4n - 180 = 0
⇒ 2n2 - n - 45 = 0
⇒ 2n2 - 10n + 9n - 45 = 0
⇒ 2n(n -5) + 9(n - 5) = 0
⇒ (2n - 9)(2n + 9) = 0
So, n = 5 (as it is positive integer)
∴ a5 = 8 + 5 × 4 = 34

Concept: Sum of First n Terms of an AP
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.3 | Q 3.06 | Page 112
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