Recent questions tagged sequences&series

Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is$14900$$15000$$14798$$1...

Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is$14900$$15000$$14798$$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 $495...

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...

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$

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

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{...

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...

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

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...

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$

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 6Se...

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 ...

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 ...

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...

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}$

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{...

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

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 ...

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{...

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,...

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{...

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{...

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

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