Sequence and SeriesMCQPYQ May 18Question 1768 of 212
All Questions

Insert two arithmetic means between 68\displaystyle 68 and 260\displaystyle 260.

Options

A132,196\displaystyle 132, 196
B130,194\displaystyle 130, 194
C70,258\displaystyle 70, 258
DNone of these
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Correct Answer

Option a132,196\displaystyle 132, 196

All Options:

  • A132,196\displaystyle 132, 196
  • B130,194\displaystyle 130, 194
  • C70,258\displaystyle 70, 258
  • DNone of these

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Detailed Solution & Explanation

Let the two arithmetic means be A1\displaystyle A_1 and A2\displaystyle A_2.
Then, the sequence 68,A1,A2,260\displaystyle 68, A_1, A_2, 260 is in A.P.
Here, the total number of terms is N=4\displaystyle N = 4.
The first term a=68\displaystyle a = 68 and the fourth term t4=260\displaystyle t_4 = 260.

Using the A.P. term formula:
t4=a+3dt_4 = a + 3d
260=68+3d260 = 68 + 3d
192=3d    d=64192 = 3d \implies d = 64

Now, calculate the two means:
A1=a+d=68+64=132A_1 = a + d = 68 + 64 = 132
A2=a+2d=68+2(64)=196A_2 = a + 2d = 68 + 2(64) = 196
So the two arithmetic means are 132\displaystyle 132 and 196\displaystyle 196.
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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