Sequence and SeriesMCQPYQ Jun 23Question 1774 of 213
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How many numbers between $74\displaystyle and $25,556 are divisible by 5\displaystyle 5?

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

✅ Option b — $5097$

All Options:

  • A$5090$
  • B$5097$
  • C$5095$
  • D$5075$

Detailed Solution & Explanation

The numbers between $74\displaystyle and $25,556 that are divisible by 5\displaystyle 5 form an A.P. series:
75,80,85,…,2555575, 80, 85, \dots, 25555
Here:
First term a=75\displaystyle a = 75
Common difference d=5\displaystyle d = 5
Last term l=25555\displaystyle l = 25555

Using the formula for the last term of an A.P.:
l=a+(n−1)dl = a + (n-1)d
25555=75+(n−1)525555 = 75 + (n-1)5
25480=(n−1)525480 = (n-1)5
n−1=5096  ⟹  n=5097n-1 = 5096 \implies n = 5097
Hence, **Option B** 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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