Number Series, Coding and DecodingMCQMTP March 22Question 2058 of 217
All Questions

The missing term of series 11,10,?,27,66,198.5\displaystyle 11, 10, ?, 27, 66, 198.5

Options

A14\displaystyle 14
B16\displaystyle 16
C21\displaystyle 21
D19\displaystyle 19
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Correct Answer

✅ Option a — 14\displaystyle 14

All Options:

  • A14\displaystyle 14
  • B16\displaystyle 16
  • C21\displaystyle 21
  • D19\displaystyle 19

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Detailed Solution & Explanation

To find the missing term of the series 11,10,?,27,66,198.5\displaystyle 11, 10, ?, 27, 66, 198.5, we analyze the multiplication and subtraction pattern of successive terms:

Let Tn\displaystyle T_n represent the n\displaystyle n-th term of the series. The pattern is defined by multiplying each term by a factor that increases by 0.5\displaystyle 0.5 at each step, and then subtracting 1\displaystyle 1:
Tn+1=Tn×(1+0.5×(n−1))−1T_{n+1} = T_n \times (1 + 0.5 \times (n-1)) - 1
Let us compute the terms sequentially:
1st term to 2nd term:
11×1.0−1=1011 \times 1.0 - 1 = 10
2nd term to 3rd term (missing term):
10×1.5−1=1410 \times 1.5 - 1 = 14
3rd term to 4th term:
14×2.0−1=2714 \times 2.0 - 1 = 27
4th term to 5th term:
27×2.5−1=66.527 \times 2.5 - 1 = 66.5
*Note:* The textbook/question lists this term as 66\displaystyle 66. This is a minor typographical error in the source material, as the correct value should be 66.5\displaystyle 66.5 to maintain the logical progression.

5th term to 6th term (using the correct value 66.5\displaystyle 66.5):
66.5×3.0−1=199.5−1=198.566.5 \times 3.0 - 1 = 199.5 - 1 = 198.5
This perfectly matches the final term given in the series, mathematically proving that the missing term is 14\displaystyle 14.

Hence, **Option A** is the correct answer.

About This Chapter: Number Series, Coding and Decoding

Paper

Paper 3: Quantitative Aptitude

Weightage

5 Marks

Key Topics

Number series, Coding & Decoding, Odd man out

This chapter covers Number series, Coding & Decoding, Odd man out and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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