Quantitative Aptitude

Number Series

2,662 Questions
All First differences and arithmetic progressions 812 Successive multiplication or division 429 Step-wise calculations 349 Squares and cubes based 338 Separate alternate positions 241 Inter-term operations 144 Mixed-operation rules 138 Unconventional pattern solving 74 Fractional and decimal operations 60 Prime number based 54 Digit operations 23

Number Series Questions

Multiple choice

If the sum of the first 𝑛 terms of an arithmetic progression is 4A whereas the sum of the first 2𝑛 terms of the same series is 11A, find the sum of the first 3𝑛 terms of the progression?

  1. 21A

  2. 15A

  3. 10A

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of n terms Sn = (n/2)(2a + (n-1)d) = 4A. Sum of 2n terms S2n = (2n/2)(2a + (2n-1)d) = 11A. 2a + (n-1)d = 8A/n. 2a + (2n-1)d = 11A/n. Subtracting: nd = 3A/n, so d = 3A/n^2. Then 2a = 8A/n - (n-1)(3A/n^2) = (8An - 3An + 3A)/n^2 = (5An + 3A)/n^2. S3n = (3n/2)(2a + (3n-1)d) = (3n/2)((5An+3A)/n^2 + (3n-1)(3A/n^2)) = (3n/2)(5An+3A + 9An-3A)/n^2 = (3n/2)(14An/n^2) = 21A.

Multiple choice

The subsequent terms in all the given three number series should follow the pattern "1 more than the square of consecutive even numbers". A. 50, 55, 72, 109, 174, 275 B. 200, 205, 222, 259, 324, 425 C. 100, 105, 122, 159, 224, 324 Which of the following series does not follow the pattern?

  1. Only C

  2. Only B

  3. Both A and B

  4. Both B and C

  5. All of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pattern: n^2 + 1 for even n (2, 4, 6, 8, 10, 12). 2^2+1=5, 4^2+1=17, 6^2+1=37, 8^2+1=65, 10^2+1=101, 12^2+1=145. Series A: 50, 55, 72, 109, 174, 275. Differences: 5, 17, 37, 65, 101. This matches. Series B: 200, 205, 222, 259, 324, 425. Differences: 5, 17, 37, 65, 101. This matches. Series C: 100, 105, 122, 159, 224, 324. Differences: 5, 17, 37, 65, 100. The last difference is 100, not 101.

Multiple choice

Find the pattern of the given series and answer the following question. ?, 6, 30, 210, 1890, 20790 If the difference between Y and the missing term of the above series is 11, and Y is greater than the missing term, then find the value of Y/2.

  1. 13

  2. 8.5

  3. 6.5

  4. 10

  5. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Series: ?, 6, 30, 210, 1890, 20790. Pattern: 6*5=30, 30*7=210, 210*9=1890, 1890*11=20790. The missing term is 6/3 = 2. If Y - 2 = 11, Y = 13. Y/2 = 6.5.

Multiple choice

A sequence consists of 50 terms and follows an arithmetic progression. The fourth term of the sequence is 10. It is also known that twice the fifth term plus three times the eighth term is equal to the sum of the tenth and fifteenth terms. What is the sum of all the terms of the sequence?

  1. 10,350

  2. 12,250

  3. 11,200

  4. 11,250
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

a + 3d = 10. 2(a+4d) + 3(a+7d) = (a+9d) + (a+14d). 2a + 8d + 3a + 21d = 2a + 23d. 3a = -6d, so a = -2d. Substitute into first: -2d + 3d = 10, so d = 10, a = -20. Sum = (n/2) * (2a + (n-1)d) = 25 * (-40 + 49*10) = 25 * 450 = 11250.