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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Straight Lines

BITSAT 2009 · Mathematics · Straight Lines

The (100^ th ) term of the sequence 1,2,2,3,3,3,4,4 , (4,4, ) is

The (100^{\text{th }}) term of the sequence 1,2,2,3,3,3,4,41,2,2,3,3,3,4,4, (4,4, \ldots) is

Options

  1. A12
  2. B13
  3. C14
  4. D15

Correct answer

C. 14

Step-by-step solution

(1st  term →1,2nd  term =2,4th  term →3,7th  term →4,11th  term →5,…\begin{aligned} & 1^{\text{st }} \text{ term } \rightarrow 1,2^{\text{nd }} \text{ term }=2,4^{\text{th }} \text{ term } \rightarrow 3, \\ & 7^{\text{th }} \text{ term } \rightarrow 4,11^{\text{th }} \text{ term } \rightarrow 5, \ldots \end{aligned}) Series is (1,2,4,7,11, \ldots) (a_n=1+\frac{n(n-1)}{2}=\frac{n^2-n+2}{2}) If n=14n=14, then (a_n=92, \mathrm{If} n=15), then an=106a_n=106.
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