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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Sequences and Series

NDA 2016 · Mathematics · Sequences and Series

Paragraph: The interior angles of a polygon of n sides are in AP....

Paragraph: The interior angles of a polygon of n sides are in AP. The smallest angle is 120∘120^{{}^{\circ}} and the common difference is 5∘5^{{}^{\circ}}.
Question: What is the largest interior angle of the polygon?

Options

  1. A160∘160^{{}^{\circ}} only
  2. B195∘195^{{}^{\circ}} only
  3. CEither 160∘160^{{}^{\circ}} or 195∘195^{{}^{\circ}}
  4. DNither 160 nor 195∘195^{{}^{\circ}}

Correct answer

A. 160∘160^{{}^{\circ}} only

Step-by-step solution

For n=9n=9 Largest angle =T9=120+(9−1)5=160=T_9=120+(9-1)^{5}=160 For n=16n=16 Largest angle =T16=120+(16−1)5=195=T_{16}=120+(16-1)^{5}=195 (Not possible).
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