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

Following two given series are in A.P. $2, 4, 6, 8 ...$ $3, 6, 9, 12 ...$ First series contains $30$ terms, while the second series contains $20$ terms. Both of the above given series contains some terms, which are common to both of them. The sum of both the above given A.P. are respectively:
  1. $(930, 630)$
  2. $(630, 930)$
  3. $(870, 580)$
  4. $(580, 870)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Series 1: 2, 4, 6... (30 terms). Sum = (30/2)(2*2 + 29*2) = 15(4+58) = 15*62 = 930. Series 2: 3, 6, 9... (20 terms). Sum = (20/2)(2*3 + 19*3) = 10(6+57) = 10*63 = 630.

Multiple choice

Suppose a series of $n$ terms is given by $\displaystyle S_{n}=a_{1}+a_{2}+...+a_{n}$ Then $\displaystyle S_{n-1}=a_{1}+a_{2}+...+a_{n-1}\left ( \forall \ n > 1 \right )$ and then we can write $\displaystyle t_{n}=S_{n}-S_{n-1} \ \forall n\geq 2$ for $ n=1 $ we have $\displaystyle S_{1}=t_{1}$ On the basis of above information answer the following questions If sum to $ n$ terms of a series is $\displaystyle an^{2}+bn$ where $a$, $b$ are constants then $ 5^{th} $ term of the series is
  1. $\displaystyle 5a+b$
  2. $\displaystyle 9a+b$
  3. $\displaystyle 9a+2b$
  4. $\displaystyle 7a+b$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sn = an^2 + bn. t(n) = Sn - S(n-1). t(5) = S(5) - S(4). S(5) = a(25) + 5b. S(4) = a(16) + 4b. t(5) = (25a + 5b) - (16a + 4b) = 9a + b.