CAT QA Preparation 2023: Check Questions & Solutions on Algebra (Progressions)

1.1000 is the second term of a geometric progression and the common ratio is r = 1/n, n= natural number. Pn is the product of n terms of the geometric progression.
P6 > P5
P6 > P7
Which option can be the possible value of n?

9
8
7
6

2.Sum of initial twelve terms is equal to the sum of the first 14 terms of the same GP. Sum of the initial 17 terms is 92.What must be the third term of the geometric progression?

90
92
94
96

3.If Sum of initial 25 terms in AP is 525, sum of the succeeding 25 terms is 725. Then the common difference is?

9/25
7/25
8/25
6/25

4.The mth term of AP be defined as Tn. The sum up to 'm' terms be defined as Sn.|T8| = |T16| &T3 is not equal to T7, Find S23?

3
2
1
0

5.a, b, c, d and e are 5 distinct numbers forming an arithmetic progression. They may or may not be consecutive terms but form the first 5 terms of the progression We know that c is the arithmetic mean of a and b, similarly d is the arithmetic mean of b and c. Which statement is correct?
i. C is the average of all 5 terms is put together.
ii. Average of a and b is not less than that of d and e.
iii. Average of b and c must be greater than that of a and d.

i and ii only
ii and iii only
i only
None of the above

6.Consider l, m, n in a G.P. such that |l + m + n| = 15. The median of these three terms is l, and m = 10. If l > n, what is the product of the first 4 terms of this G.P.?

38,000
40,000
42,000
44,000

7.If 9 times the 9th term of the A.P. is equal to 4 times the 4th term of an A.P., what is 13 times the 13th term of this A.P.?

2
1
0
-1

8.Sequence M is defined by mn = mn-1 + 3, p1 = 11, Sequence J is defined as jn = jn-1 – 4, j3 = 103. If jk > jk+2, Find the minimum value k can have?

12
13
14
15

9.The sum of n terms of A.P. = {56, 58, 60..…} is less than the sum of 2n terms of A.P. {1, 5, 9, 13…..}. Find the minimum value of n?

9
8
7
6

10.m, n, p and q are in A.P., What type of progression is npq, mpq, mnq and mnp?

A.P.
H.P.
G.P.
None of the Above

11.The 8th term in an AP is 2 more than thrice the second term while the second term in an AP is 8. Find the of the first 8 terms of this AP.

120
123
124
127

12.If Kp = p3 + p2 + p + 1 , where Kp denotes the sum of the first p terms of a series and Tn= 291, then n is equal to?

27
28
29
30

13.12 is the sum of infinite terms of a GP. If the first term is 8, Find the 4th term of this progression?

14.Find the sum of 2² + 2 * 3² + 3 * 4² + 4 * 5² .....10 * 11²

3840
3850
3860
3870

15.The salaries earned by Tom and Bob in different years are in A.P. If the ratio of the total salary earned by them in ‘z’ number of years are (4z+1) : (2z+17). Find the ratio of amount earned by both in the 7th year

63 : 53
73 : 63
53 : 43
None of the above

16..In 4 years, a total of INR 2000 is invested in government bonds by Sam. Suppose these investments are in A.P. 1200000 is the sum of squares of the investments. Find the investment made by Sam each year. It is given that he always invest more than the previous year.

200,300,400,500
200,500,8001100
300,500,700,900
200,400,600,800

17.Sam invested different amounts during the year on shares. S1, S2, S3……….Sp are different sums of ‘m’ amounts invested in ‘mp’ years. If the amounts invested during the years are in A.P whose first terms are 1,2,3…..p and common difference are 1,3,5…..,(2p-1) respectively then find the total amount invested by Sam in ‘p’ years.

mp/2(mp+1)
mp/(mp+1)
mp/3(mp+2)
None of the above

18.Find the sum of the progression .4 + .44 + .444…to m terms?

5/80(9m-1+1/10n )
50/61(9m-1+1/10n )
7/81(9m-1+1/10n )
4/81(9m-1+1/10n )

19.If the equation lx2 + 2mx + n= 0 and ax2 + 2bx + c = 0 have a common root,then in what type of progression is a/l, b/m , c/n

A.P.
H.P.
G.P.
None of the above

20.If the first 3 terms among 4 positive integers are in A.P and the last 3 terms are in G.P., then find the sum. Also, the difference between the first and last term is 40.

170
172
174
176

21.An arithmetic progression has 30 terms. The sum of first 13 terms is equal to the sum of the first 27 terms . Which of the following statement should be true?

Sum of all terms in the progression is 0
The sum of all terms will be negative
0 is 14th term of the progression
None of the above

22.A={ 4, 9, 14, 19, ……. 999}
B={ 6, 13, 20, 27,...... 909}
If C= A ∩B, how many sets does C have?

4^13
4^12
5^13
6^12

23.How many arithmetic progressions of 6 term can be formed from the first 25 natural numbers such that common difference of the AP is a factor of the 6th term.

29
30
31
0

24.The internal angles of a convex polygon are in arithmetic progression with a common difference of 10 degrees. How many sides does the polygon has if the smallest angle is 100 degrees.

7
8
9
10

25. Find the common term in the sequence below?
3,7,11,15,19…….191
9,14,19,24……….224

9
19
24
15