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

$a, 2a -1, 3a -2, 4a -3, . . .$ For a particular number $a$, the first term in the sequence above is equal to $a$ and each term thereafter is $7$ greater than the previous term. What is the value of the $16th$ term in the sequence?
  1. $113$
  2. $110$
  3. $96$
  4. $120$
  5. $130$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sequence is an arithmetic progression with first term a and common difference 7. The 16th term is a + (16-1)*7 = a + 105. The first term is a, second is 2a-1. So 2a-1 = a+7, which means a=8. The 16th term is 8 + 105 = 113.

Multiple choice

Find the $11$th term of the sequence $5,2,-1,-4,......$
  1. $-25$
  2. $-28$
  3. $-22$

  4. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is an arithmetic progression with first term a = 5 and common difference d = 2 - 5 = -3. The nth term is given by a + (n - 1)d. For the 11th term, 5 + (11 - 1)(-3) = 5 + 10(-3) = 5 - 30 = -25.

Multiple choice

The sum to $50$ terms of the series $\dfrac {1}{2} + \dfrac {3}{4} + \dfrac {7}{8} + \dfrac {15}{16} + ....$ is equal to
  1. $2^{50} - 51$
  2. $1 - 2^{-50}$
  3. $2^{-50}+49$
  4. $2^{50} - 1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The series is 1/2 + 3/4 + 7/8 + 15/16 + ... which can be written as (1 - 1/2) + (1 - 1/4) + (1 - 1/8) + (1 - 1/16) + ... to 50 terms. This equals 50 - (1/2 + 1/4 + 1/8 + ... + 1/2^50). The sum of the geometric series is (1/2 * (1 - (1/2)^50)) / (1 - 1/2) = 1 - 1/2^50. Total sum = 50 - (1 - 1/2^50) = 49 + 1/2^50.

Multiple choice

The sum of infinite terms of the following series $1+\dfrac {4}{5}+\dfrac {7}{{5}^{2}}+\dfrac {10}{{5}^{3}}+..$ will be
  1. $\dfrac {3}{16}$
  2. $\dfrac {25}{8}$
  3. $\dfrac {35}{4}$
  4. $\dfrac {35}{16}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

S = 1 + 4/5 + 7/5^2 + 10/5^3 + ... This is an arithmetico-geometric series. S = 1 + 4/5 + 7/25 + 10/125 + ... S/5 = 1/5 + 4/25 + 7/125 + ... Subtracting: 4S/5 = 1 + 3/5 + 3/25 + 3/125 + ... 4S/5 = 1 + (3/5) / (1 - 1/5) = 1 + (3/5) / (4/5) = 1 + 3/4 = 7/4. S = (7/4) * (5/4) = 35/16.