Progressions

Q.

Convert $25$ degree Celsius into Fahrenheit.

Q.

Two numbers are in the ratio $5:3$ if they differ by $18$ what are the numbers.

Q.

The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2 feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid on the one-third of the remaining and blue tiles on the rest, how many blue tiles will be there?

1. 16

2. 24

3. 32

4. None of these

5. 48

Q.

Let $a_1,a_2,a_3,...$be a sequence of positive integers in arithmetic progression with common difference $2$. Also, let $b_1,b_2,b_3,...$ be a sequence of positive integers in geometric progression with common ratio $2$. If $a_1=b_1=c$, then the number of all possible values of $c$, for which the equality $2\left(a_1+a_2+a_3+...+a_n\right)=b_1+b_2+b_3+,...+b_n$​ holds for some positive integer $n$, is _____

Q.

The sum of three consecutive multiples of 3 is 72. What is the largest number?

1. 21

2. 24

3. 27

4. 36

5. 28

Q.

Let $a_{1,}{a}_2,a_3,..$ be terms of an A.P. If $\frac{a_1+a_2+...+a_p}{a_1+a_2+...+a_q}=\frac{p^2}{q^2}$, $p$ not equal to $q$, then $\frac{a_6}{a_{21}}$ equals

1. $\frac{7}{2}$

2. $\frac{2}{7}$

3. $\frac{11}{41}$

4. $\frac{41}{11}$

Q. The third term of a GP is 3. Find the product of first five terms.

1. 81
2. 243
3. 256
4. 343

Q. The L.C.M. and H.C.F. of the number 28 and 42 are in the ratio _____.

1. 9 : 3
2. 6 : 1
3. 2 : 3
4. 3 : 2
5. 7 : 2

Q.

An AP consists of $37$ terms. The sum of the three middlemost terms is $225$ and the sum of the last three is $429$. Find the AP.

Q.

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

1. $2+\sqrt{3}$

2. $3+\sqrt{2}$

3. $2-\sqrt{3}$

4. $2+\sqrt{2}$

Q. A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible? (CAT 2006)

1. 3
2. 4
3. 5
4. 6
5. 7

Q.

Two natural numbers are in the ratio 3:5 and their product is 2160. The smaller of the numbers is

1. 24

2. 30

3. 36

4. 42

5. none

Q. The sum of 3rd and 15th elements of an arithmetic expression is equal to the sum of 6th, 11th and 13th elements of the progression. Then which element of the series should necessarily be equal to zero(CAT 2003)

1. 9th
2. 12th
3. None of these
4. 1st

Q.

The sum of five consecutive numbers is 190. What is the sum of the largest and the smallest number?

1. 77

2. 73

3. None of these

4. 76

Q. Choose the most appropriate option to replace (?).
8, 15, 36, 99, 288, ?

1. 368
2. 676
3. 855
4. 908
5. None of the above

Q.

The sum of all terms of the arithmetic progression having ten terms except for the first term is 99, and except for the sixth term, 89. Find the third term of the progression if the sum of the first and the fifth term is equal to 10?

1. 15

2. 5

3. 8

4. 10

Q. There are 256 players in a chess tournament (singles). Two players play a match. Matches are played on a knockout basis, the loser is eliminated after each match. How many matches need to be played to declare a winner? There is no draw.___

Q.

The runs scored in a cricket match by $11$ players is as follows:$6,15,120,50,100,80,10,15,8,10,15$ Find the mean, mode and median of this data. Are the three same?

Q.

Which term of the AP: $121,117,113,...$ is its first negative term?

Q.

The sum of first two terms of a G.P is $\frac{5}{3}$ and the sum to infinite terms is 3. What is the first term?

1. 
2. 1
3. 6
4. 9

Q. The fourth term of an arithmetic progression is 8. What is the sum of first 7 terms of the arithmetic progression?(CAT 1994)

1. 7
2. 64
3. 56
4. Cannot be determined

Q.

The ratio of the sums of first $n$ even number and $n$ odd number will be

1. $1:n$

2. $\left(n+1\right):1$

3. $\left(n+1\right):n$

4. $\left(n-1\right):1$

Q. How many terms of the A.P 1, 4, 7, ... are needed to give the sum 925?

1. 20
2. 22
3. 24
4. 25

Q. An equilateral triangle is drawn by joining the midpoints of the sides of another equilateral triangle. A third equilateral triangle is drawn inside the second one joining the midpoints of the sides of the second equilateral triangle, and the process continues infinitely. Find the sum of the perimeters of all the equilateral triangles, if the side of the largest equilateral triangle is 24 units.

1. 144 units
2. 288 units
3. 36 units
4. 72 units

Q. Insert the missing number
1, 1, 4, 8, 9, 27, 16, ___

1. 64
2. None of the above
3. 36
4. 125
5. 25

Q. There are four numbers such that first three of them form an Arithmetic Progression and the last three form a Geometric Progression. The sum of the first and the third is 2 and that of second and fourth is 26. What is the sum of first and fourth number?

1. none of these
2. $85\frac{13}{25}$
3. $25\frac{73}{85}$
4. 83

Q. Product of the fourth term and the fifth term of an arithmetic progression is 456. Division of the ninth term by the fourth term of the progression gives Quotient as 11 and the remainder as 10. Find the first term of the progression.

1. - 52
2. - 42
3. - 56
4. - 66

Q. Sum of three consecutive terms in a GP is 42 and their product is 512. Find the largest of these numbers.

1. 32
2. 64
3. 128
4. none of these

Q. What is the maximum sum of the terms in the arithmetic progression 25, 24, 23, 22.......?

1. 325
2. 345
3. 350
4. 332.5

Q.

If first three terms of sequence $\frac{1}{16},a,b,\frac{1}{6}$ are in geometric series and last three terms are in harmonic series, then the value of $a$ and $b$ will be

1. $a=-\frac{1}{4},b=1$

2. $a=\frac{1}{12},b=\frac{1}{9}$

3. $A$ and $B$ both are true

4. None of these