Sequence and SeriesMCQMTP Nov 19Question 1792 of 212
All Questions

If three AM's between 3\displaystyle 3 and 11\displaystyle 11, they are

Options

A4,6,8\displaystyle 4, 6, 8
B3,5,7\displaystyle 3, 5, 7
C5,7,9\displaystyle 5, 7, 9
D11/2,15/2,19/2\displaystyle 11/2, 15/2, 19/2
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Correct Answer

Option c5,7,9\displaystyle 5, 7, 9

All Options:

  • A4,6,8\displaystyle 4, 6, 8
  • B3,5,7\displaystyle 3, 5, 7
  • C5,7,9\displaystyle 5, 7, 9
  • D11/2,15/2,19/2\displaystyle 11/2, 15/2, 19/2

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Detailed Solution & Explanation

Let the three arithmetic means be A1,A2,A3\displaystyle A_1, A_2, A_3.
Then, the sequence 3,A1,A2,A3,11\displaystyle 3, A_1, A_2, A_3, 11 is in A.P.
Here:
First term a=3\displaystyle a = 3
Total number of terms N=5\displaystyle N = 5
Fifth term t5=11\displaystyle t_5 = 11.

Using the A.P. formula:
t5=a+4dt_5 = a + 4d
11=3+4d11 = 3 + 4d
8=4d    d=28 = 4d \implies d = 2

Now, calculate the three means:
A1=a+d=3+2=5A_1 = a + d = 3 + 2 = 5
A2=a+2d=3+4=7A_2 = a + 2d = 3 + 4 = 7
A3=a+3d=3+6=9A_3 = a + 3d = 3 + 6 = 9
So the three AMs are 5,7,9\displaystyle 5, 7, 9.
Hence, **Option C** 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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