Sequence and SeriesMCQMTP June 24 Series IQuestion 1813 of 212
All Questions

The first, second and seventh term of an AP are in G.P. and the common difference is 2\displaystyle 2, the 2nd\displaystyle 2^{nd} term of A.P. is:

Options

A5/2\displaystyle 5/2
B2
C3/2\displaystyle 3/2
D1/2\displaystyle 1/2
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Correct Answer

✅ Option a — 5/2\displaystyle 5/2

All Options:

  • A5/2\displaystyle 5/2
  • B2
  • C3/2\displaystyle 3/2
  • D1/2\displaystyle 1/2

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Detailed Solution & Explanation

Let the first term of the A.P. be a\displaystyle a and the common difference be d=2\displaystyle d = 2.
The terms are:
First term: t1=a\displaystyle t_1 = a
Second term: t2=a+d=a+2\displaystyle t_2 = a + d = a + 2
Seventh term: t7=a+6d=a+12\displaystyle t_7 = a + 6d = a + 12

Since t1,t2,t7\displaystyle t_1, t_2, t_7 are in G.P.:
(t2)2=t1⋅t7(t_2)^2 = t_1 \cdot t_7
(a+2)2=a(a+12)(a+2)^2 = a(a+12)
a2+4a+4=a2+12aa^2 + 4a + 4 = a^2 + 12a
8a=4  ⟹  a=128a = 4 \implies a = \frac{1}{2}

The second term of the A.P. is:
t2=a+2=12+2=52t_2 = a + 2 = \frac{1}{2} + 2 = \frac{5}{2}
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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