# Recent questions tagged sequences&series

1

Direction for questions: Answer the questions based on the following information. A series $S_{1}$ of five positive integers is such that the third term is half the first...

2

3

4

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 $4...

5

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...

6

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$

7

Find the value of the expression $1-6+2-7+3-8+\dots\dots$ to $100$ terms.$-250$$-500$$-450$$-300$

8

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{...

9

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 \ri...

10

The greatest number of four digits which is divisible by each one of the numbers $12$, $18$, $21$ & $28$, is :$9848$$9864$$9828$$9636$

11

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...

12

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 particu...

13

14

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$

15

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...

16

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$

17

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...

18

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...

19

Study the following series Ⅰ and Ⅱ comprising letters/digits/symbols and answer the questions given below.Series I : N P Q * 5 4 B Z \$ # 3 7 D 9 A ? F 8 G H 1 + D K...

20

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 ...

21

22

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...

23

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}$

24

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{...

25

Shoes is related to Shining in the same way as Pant is related to$\dots$?StitchingWearingKeepingBuying

26

Find the missing term:$60,40,55,45,50,50,?$$45$$50$$55$$60$

27

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 ...

28

Find the missing alphabet:$T,r,O,m,J,?$$h$$i$$I$$g$

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{...

30

31

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,...

32

33

34

Have a look at the series: $26,24,20,18,14,\dots$What number should come next?$10$$12$$13$$16$

35

Have a look at the series: $4,7,5,8,6,9,\dots\dots,\dots$What number should come next?$7$$9$$10$$13$

36

Find the wrong number in the sequence$125,127,130,135,142,153,165$$130$$142$$153$$165$

37

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)$

38

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{a...

39

40

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$