Sequence and SeriesMCQMTP June 2023 Series IIQuestion 1812 of 213
All Questions

If $20$ AMs. are inserted between $3\displaystyle and $51 then sum of these $20$ A.M.s is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 540

All Options:

  • A540
  • B1080
  • C270
  • DNone of these

Detailed Solution & Explanation

The sum of N\displaystyle N arithmetic means inserted between two numbers a\displaystyle a and b\displaystyle b is equal to N\displaystyle N times the single arithmetic mean between a\displaystyle a and b\displaystyle b:
Sum=N⋅(a+b2)Sum=N\displaystyle \text{Sum} = N ⋅\displaystyle \cdot \left(a+b2\displaystyle \frac{a+b}{2}\right)
Substitute the given values (N=20,a=3,b=51\displaystyle N=20, a=3, b=51):
Sum=20⋅(3+512)=20⋅27=540Sum=20\displaystyle \text{Sum} = 20 ⋅\displaystyle \cdot \left(3+512\displaystyle \frac{3+51}{2}\right) = 20 ⋅\displaystyle \cdot 27 = 540
Hence, **Option A** is the correct answer.

About This Chapter: Sequence and Series

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Arithmetic & Geometric Progressions

This chapter covers Arithmetic Progressions (AP) and Geometric Progressions (GP). Students learn how to find the nth term, sum of n terms, arithmetic/geometric means, and sum to infinity of a GP.

View Official ICAI Syllabus

Exam Strategy Tip

For complex 'sum of series' questions, a great hack is to substitute n = 1 and n = 2 into the question and the options to see which one matches, completely bypassing the formula.

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