Sequence and SeriesMCQMTP Dec 22 Series IIQuestion 1806 of 212
All Questions

Sum lying from 100\displaystyle 100 to 300\displaystyle 300 which is divisible by 4\displaystyle 4 and 5\displaystyle 5 is

Options

A2000
B2100
C2200
D2300
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option c2200

All Options:

  • A2000
  • B2100
  • C2200
  • D2300

Ad

Detailed Solution & Explanation

A number divisible by both 4\displaystyle 4 and 5\displaystyle 5 must be divisible by their L.C.M., which is 20\displaystyle 20.
The numbers divisible by 20\displaystyle 20 lying from 100\displaystyle 100 to 300\displaystyle 300 inclusive are:
100,120,140,,300100, 120, 140, \dots, 300
Here:
First term a=100\displaystyle a = 100
Common difference d=20\displaystyle d = 20
Last term l=300\displaystyle l = 300.

Using the last term formula:
l=a+(n1)dl = a + (n-1)d
300=100+(n1)20300 = 100 + (n-1)20
200=(n1)20    n1=10    n=11200 = (n-1)20 \implies n-1 = 10 \implies n = 11

The sum is:
S11=112[a+l]=112[100+300]=112[400]=2200S_{11} = \frac{11}{2} [a + l] = \frac{11}{2} [100 + 300] = \frac{11}{2} [400] = 2200
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.

Related Comparison Tables

More Questions from Sequence and Series

Ready to Master Sequence and Series?

Practice all 212 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free