# Recent questions tagged sequences&series 1 vote
1
Consider a sequence of real numbers $x_{1}, x_{2}, x_{3}, \dots$ such that $x_{n+1} = x_{n} + n – 1$ for all $n \geq 1.$ If $x_{1} = -1$ then $x_{100}$ is equal to $4950$ $4850$ $4849$ $4949$
1 vote
2
For a sequence of real numbers $x_{1}, x_{2}, \dots , x_{n},$ if $x_{1} – x_{2} + x_{3} – \dots + (-1)^{n+1} x_{n} = n^{2} + 2n$ for all natural numbers $n,$ then the sum $x_{49} + x_{50}$ equals $2$ $-2$ $200$ $-200$
1 vote
3
If $x_{0} = 1, x_{1} = 2$ and $x_{n+2} = \dfrac{1 + x_{n+1}}{x_{n}}, n = 0, 1, 2, 3, \dots ,$ then $x_{2021}$ is equal to $1$ $3$ $4$ $2$
4
Find the value of the expression $1-6+2-7+3-8+\dots\dots$ to $100$ terms. $-250$ $-500$ $-450$ $-300$
5
The value of the following expression : $\left [ \frac{1}{2^{2}-1} \right ]+\left [ \frac{1}{4^{2}-1} \right ]+\left [ \frac{1}{6^{2}-1} \right ]+\dots\dots+\left [ \frac{1}{20^{2}-1} \right ]$ is : $\frac{10}{21}$ $\frac{13}{27}$ $\frac{15}{22}$ $\frac{22}{15}$
6
The sum of first $n$ terms of an $A.P$. whose first term is $\pi$ is zero. The sum of next $m$ terms is : $\frac{ \pi m \left(m+n \right)}{n-1}$ $\frac{ \pi n \left(m+n \right)}{1-n}$ $\frac{ \pi m \left(m+n \right)}{1-n}$ $1$
7
The greatest number of four digits which is divisible by each one of the numbers $12$, $18$, $21$ & $28$, is : $9848$ $9864$ $9828$ $9636$
1 vote
8
Of the three numbers, the sum of the first two is $45$; the sum of the second and third is $55$ and the sum of the third and thrice the first is $90$. The third number is : $20$ $25$ $30$ $35$
1 vote
9
Study the following information carefully to answer the questions given below: A number sorting machine when given an input of numbers, rearranges the numbers in a particular manner step by step as indicated below till all the numbers are arranged in a particular order. Given below is an illustration of this ... $\text{17 24 47 62 92 86 42 79}$ $\text{17 47 62 86 24 42 79 92}$
1 vote
10
Study the following information carefully to answer the questions given below: A number sorting machine when given an input of numbers, rearranges the numbers in a particular manner step by step as indicated below till all the numbers are arranged in a particular order. Given below is an illustration of ... $\text{17 32 82 69 93 43 49 56 99 106}$ Cannot be determined
1 vote
11
Which of the following will be the middle digit of the middle number after reversing the digits of the following numbers ? $\text{389 675 493 728 536}$ $3$ $2$ $8$ $9$
1 vote
12
Which of the following does not fit in the letter number series given below? $G$ $4$ $T$ $J$ $10$ $R$ $M$ $20$ $P$ $P$ $43$ $N$ $S$ $90$ $L$ $J$ $10$ $R$ $M$ $20$ $P$ $P$ $43$ $N$ $G$ $4$ $T$
13
The value of $\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+ \dots \dots \dots+\dfrac{1}{90}$ is: $\dfrac{1}{5}\\$ $\dfrac{2}{5} \\$ $\dfrac{3}{5} \\$ $1$
14
The sum of the squares of the fifth and the eleventh term of an AP is $3$ and the product of the second and fourteenth term is equal to $x$. Find the product of the first and fifteenth term of an AP. $\dfrac{(58x-39)}{45} \\$ $\dfrac{(98x-39)}{72} \\$ $\dfrac{(116x-39)}{90} \\$ $\dfrac{(98x-39)}{90}$
15
If $S_1,S_2,S_3,\dots\dots,S_m$ are the sum of first $n$ terms of $m$ arithmetic progressions, whose first terms are $1,4,9,16,\dots,m^{2}$ and common differences are $1,2,3,4,\dots m$ respectively, then the value of $S_1+S_2+S_3+\dots \dots +S_m$ is : $\dfrac{mn(m+1)}{2} \\$ $\dfrac{mn(2m+1)}{3} \\$ $\dfrac{mn[3(m+1)+1]}{6} \\$ $\dfrac{mn(m+1)(4m+3n-1)}{12}$
16
Study the following series Ⅰ and Ⅱ comprising letters/digits/symbols and answer the questions given below. $\textbf{Series I :}$ N P Q * 5 4 B Z \$# 3 7 D 9 A ? F 8 G H 1 + D K 6$ ... symbols from each series are counted separately, which of the following is lowest in count? Symbols in series I Letters in series I Digits in series II Symbols in series II
1 vote
17
Study the following series Ⅰ and Ⅱ comprising letters/digits/symbols and answer the questions given below. $\textbf{Series I :}$ N P Q * 5 4 B Z \$# 3 7 D 9 A ? F 8 G H 1 + D K 6$ ... preceded by a letter together with the number of letters in Series II which are immediately preceded by a symbol and immediately followed by a letter? $5$ $4$ $1$ $3$
1 vote
18
Study the following series Ⅰ and Ⅱ comprising letters/digits/symbols and answer the questions given below. $\textbf{Series I :}$ N P Q * 5 4 B Z \$# 3 7 D 9 A ? F 8 G H 1 + D K 6$ ... of the following pairs of elements will indicate $16$- th element from the left and the $8$^th element to its left respectively? $A,Q$ $3,Q$ $3,Z$ $A,Z$
1 vote
19
How many $9$’s are there in the following number sequence which are immediately preceded by $3$ but not immediately followed by $4$? $\text{2 3 9 5 1 3 9 6 7 3 9 4 8 9 3 4 9 3 2 3 9 8 3 9 3}$ $3$ $2$ $1$ $4$
1 vote
20
In a certain code $\text{UPGRADE}$ is written as $\text{WNIPCBG}$. How is $\text{DROWN}$ written in that code? $\text{BTMYL}$ $\text{BPMYL}$ $\text{BTQYL}$ $\text{FPQUP}$
1 vote
21
In a certain $\text{STABILISE}$ is written as $\text{UVCDKNKUG.}$ How is $\text{ORGANISE}$ written in that code? $\text{QTICPKUG}$ $\text{QTICPKUH}$ $\text{QTIBPKUG}$ $\text{QTICPKUJ}$
1 vote
22
Shoes is related to Shining in the same way as Pant is related to$\dots$? Stitching Wearing Keeping Buying
1 vote
23
Find the missing term: $60,40,55,45,50,50,?$ $45$ $50$ $55$ $60$
1 vote
24
If the consonants in the word ‘DROVE’ are first arranged alphabetically and the vowels are put in between two pairs of consonants in the alphabetical order, which of the following will be the fourth from the right end after the rearrangement? $D$ $E$ $R$ $O$
1 vote
25
Find the missing alphabet: $T,r,O,m,J,?$ $h$ $i$ $I$ $g$
1 vote
26
In the following question, various terms of a letter series are given with one term missing as shown by (?). Choose the missing term out of the given alternatives. $\text{C,F,J,O,?,B}$ $\text{S}$ $\text{T}$ $\text{U}$ $\text{V}$
1 vote
27
In the following question, various terms of a letter series are given with one term missing as shown by (?). Choose the missing term out of the given alternatives. $\text{ABP, CDQ, EFR, }(\dots?\dots)$ $\text{GHS}$ $\text{GHT}$ $\text{HGS}$ $\text{GHR}$
1 vote
28
In the following question, various terms of a letter series are given with one term missing as shown by (?). Choose the missing term out of the given alternatives. DF, GJ, KM, NQ, RT, ? UW YZ XZ UX
1 vote
29
In the following question, various terms of a letter series are given with one term missing as shown by (?). Choose the missing term out of the given alternatives. $\text{T,r,O,m,J,?}$ $\text{h}$ $\text{i}$ $\text{I}$ $\text{g}$
30
In the following question, various terms of a letter series are given with one term missing as shown by (?). Choose the missing term out of the given alternatives. $\text{C,G,L,R,?}$ $\text{Y}$ $\text{S}$ $\text{U}$ $\text{Z}$
1 vote
31
Have a look at the series: $26,24,20,18,14,\dots$ What number should come next? $10$ $12$ $13$ $16$
1 vote
32
Have a look at the series: $4,7,5,8,6,9,\dots\dots,\dots$ What number should come next? $7$ $9$ $10$ $13$
1 vote
33
Find the wrong number in the sequence $125,127,130,135,142,153,165$ $130$ $142$ $153$ $165$
1 vote
34
Have a look at the series : $2,1,(1/2),(1/4),\dots$ What number should come next? $(1/3)$ $(1/8)$ $(2/8)$ $(1/16)$
1 vote
35
In the following letter series, some of the letters are missing which are given in that order as one of the alternatives below it. Choose the correct alternative. $\text{abca _ bcaab _ aa _ caa _ c}$ $\text{bbac}$ $\text{bbaa}$ $\text{acbb}$ $\text{acac}$
1 vote
36
In the following letter series, some of the letters are missing which are given in that order as one of the alternatives below it. Choose the correct alternative. $\text{aaa_bb_ aab_baaa_bb}$ $\text{abab}$ $\text{bbaa}$ $\text{babb}$ $\text{baab}$
1 vote
37
In the following questions, one term in the number series is wrong. Find out the wrong term. $52,51, 48, 43, 34, 27, 16$ $51$ $48$ $34$ $43$
1 vote
In the following question, one term in the number series is wrong. Find out the wrong term. $125, 126, 124, 127, 123, 129$ $123$ $124$ $126$ $129$
In the following question, find out the correct answer from the given alternatives. If $\text{TABLE}$ is coded as $\text{GZYOV}$, how is $\text{JUICE}$ coded? $\text{OZLFJ}$ $\text{QFRXV}$ $\text{HOFAD}$ $\text{QZHMT}$
In the following question, find out the correct answer from the given alternatives. If in a certain language $\text{MECHANICS}$ is coded as $\text{HCEMASCIN}$, how is $\text{POSTER}$ coded in that code? $\text{OPTSRE}$ $\text{SOPRET}$ $\text{RETSOP}$ $\text{TERPOS}$