Sequence

Q. The sum of first n odd natural numbers is

(a) 2n − 1

(b) 2n + 1

(c) n²

(d) n² − 1

Q.

Q.

Which number would replace the question mark in the series? $7,12,19,?,39$

Q.

The branch of mathematics that deals with the study of numbers is called

Q.

The nth term of the sequence 1, 3, 7, 15, ... can be written as

1. $2^n$ - 1

2. $2^n$ + 1

3. $2^{n-1}$ - 1

4. $2^{n-1}$ + 1

Q. The sum of first n terms of an AP., is zero , show that the sum of next m terms is -am(m+n)/n-1, a being the first term

Q. Tom, Jerry, and Harry are three friends. They keep saying their names at regular intervals. While Tom says his name every 12 seconds, Jerry and Harry say their names every 30 and 42 seconds, respectively. If they start by saying their names together, then after what time will they all say their names in unison next?

1. 420

Q.

Re. 1 and Rs. 5 coins are available (as many required). Find the smallest payment which cannot be made by these coins, if not more than 5 coins are allowed.

1. 18

2. 14

3. 3

4. 12

Q.

How many terms of the arithmetic sequence 5, 7, 9, …. should be added to get 140?

Q.

Multiply each odd number by 2 and add 1. If these numbers are written in order, does it form and arithmetic sequence? Write the algebraic form of this sequence. Now consider the odd numbers not in this sequence. Do they form and arithmetic sequence? What is its algebraic form?

Q. 5. proove that:4cos12 .cos48.cos72=cos36

Q.

Write the number of chords in each figure as a sequence.

Do they follow arithmetic sequence?

1. 1, 3, 6, 9; Yes

2. 1, 3, 6, 9; No

3. 1, 3, 6, 10; Yes

4. 1, 3, 7, 10; No

Q. How to represent \sqrt{3.6 } on a number lin

Q.

The nth term of the sequence 1, 3, 7, 15 can be written as

1. 2ⁿ + 1

2. 2ⁿ - 1

3. 3ⁿ - 1

4. 2^n-1 + 1

Q.

A sequence starts from $\frac{1}{2}$ and $\frac{3}{4}$ is added to every term. Find the sequence.

1. None

2. $\frac{1}{2},\frac{5}{4},\frac{6}{4}\cdots \cdots$

3. $\frac{1}{2},1,\frac{5}{4}\cdots \cdots$

4. $\frac{1}{2},\frac{5}{4},2,\frac{11}{4},\frac{14}{4}\cdots \cdots$

Q. What is the nth term of the sequence

Q. The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after _____ decimal place(s).

1. 1
2. 2
3. 3
4. 4

Q. 18.In an A., the sum of first ten terms is-150 and the sum of its next ten terms is -550. Find the A.P.

Q. 50. The digits of a positive number of three digits are in AP and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.

Q. Write the sum of first n even natural numbers.

Q. X-1x=2 XX+1XxX=?

Q. An artist is drawing a some figures with geometric shapes and curves. He follows a pattern in his drawing, but he misses a figure as shown below. Let's try to fill the missing figure to complete the pattern.

Q. 1.If A = x1x2x3 and B = y1y2y3 be two three digit numbers, then the number of pairs of A and B that can be formed so that A can be subtracted from B without borrowing.

Q. Write the sum of first n odd natural numbers.

Q.

The digits of $\pi$ in its decimal form written as a sequence is

1. None

2. 1, 3, 4, 1, 5, 9, 2, 6 ..........

3. 3, 1, 4, 1, 5, 9, 2, 6 ..........

4. 1, 4, 1, 5, 9, 6 ........

Q. Find the least positive value of $x$ such that $147$ $\equiv$ $(x+5)\left(\text{mod}7\right)$.

1. $2$
2. $3$
3. $4$
4. $5$

Q. pointing to a woman in a photo, ranjit said, the only daughter of her grandfather is my wife". how is ranjit related to that woman?

Q.

A number sequence which leaves the remainder 0 on dividing by 7 is

1. 7, 20, 27, ...

2. 0, 7, 13, ...

3. 14, 21, 28, 35, ...

4. None

Q. Match the following with their absolute values

1. 4
2. $\frac{2}{3}$
3. 0
4. $\frac{3}{2}$

Q.

a2=31/4 a31=1/2 an =-30/2 find n