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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Sequences and Series

NDA 2013 · Mathematics · Sequences and Series

The sum of the first five terms and the sum of the first ten terms...

The sum of the first five terms and the sum of the first ten terms of an AP are same. Which one of the following is the correct statement?

Options

  1. AThe first term must be negative
  2. BThe common difference must be negative
  3. CEither the first term or the common difference is negative but not both
  4. DBoth the first term and the common difference are negative

Correct answer

C. Either the first term or the common difference is negative but not both

Step-by-step solution

Let first term and common difference are aandda and d respectively. Sum of first five terms = Sum of first ten terms 52(2a+(5−1)d)=102(2a+(10−1)d) or, 5(a+2d)=5(2a+9d) or, a+7d=0\begin{aligned} & \frac{5}{2}(2 a+(5-1) d)=\frac{10}{2}(2 a+(10-1) d) \\ & \text{ or, } 5(a+2 d)=5(2 a+9 d) \\ & \text{ or, } a+7 d=0 \end{aligned} This is true, only when either aorda or d is negative but not both together.
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