Practice Questions for Algebra - Progressions

1. PE 3 - Progressions | Algebra - Progressions

Thirty-one magazines are arranged from left to right in order of increasing prices. The price of each magazine differs by Rs. 2 from that of each adjacent magazine. For the price of the magazine at the extreme right a customer can buy the middle magazine and an adjacent one. Then:

(a)
The adjacent magazine referred to is at the left of the middle magazine.
(b)
The middle magazine sells for Rs. 36.
(c)
The most expensive magazine sells for Rs. 64.
(d)
None of these

2. PE 3 - Progressions | Algebra - Progressions

Given the set of n numbers, n > 1, of which one is 1− 1/n, and all the others are 1. The arithmetic mean of the n numbers is

(a)
1
(b)
n - 1/n
(c)
n - 1/n²
(d)
1 - 1/n²

3. PE 3 - Progressions | Algebra - Progressions

The angles of a pentagon are in arithmetic progression. One of the angles, in degrees, must be:

(a)
108
(b)
90
(c)
72
(d)
54

4. PE 3 - Progressions | Algebra - Progressions

If x_k+1= x_k+ 1/2 for k = 1, 2, …, n-1 and x₁= 1, find x₁+ x₂+ ⋯ + x_n.

(a)
(n + 3)/2
(b)
(n² - 1)/2
(c)
(n² - n)/2
(d)
(n² + 3n)/4

5. PE 3 - Progressions | Algebra - Progressions

Three numbers a, b, c, non-zero, form an arithmetic progression. Increasing a by 1 or increasing c by 2 results in a geometric progression. Then b equals:

(a)
16
(b)
14
(c)
12
(d)
10

6. PE 3 - Progressions | Algebra - Progressions

The sum to infinity of $\frac{1}{7}$ + $\frac{2}{7^{2}}$ + $\frac{1}{7^{3}}$ + $\frac{2}{7^{4}}$ + ... is:

(a)
1/24
(b)
5/48
(c)
1/16
(d)
None of these

7. PE 3 - Progressions | Algebra - Progressions

If the sum of the first ten terms of an arithmetic progression is four times the sum of the first five terms, then the ratio of the first term to the common difference is:

(a)
1 : 2
(b)
2 : 1
(c)
1 : 4
(d)
4 : 1

8. PE 3 - Progressions | Algebra - Progressions

A saint has a magic pot. He puts one gold ball of radius 1 mm daily inside it for 10 days. If the weight of the first ball is 1 gm and if the radius of a ball inside the pot doubles every day, how much gold will the saint have gained at the beginning of 10^th day?

(a)
(2³⁰ – 69)/7 gm
(b)
(2³⁰ + 69)/7 gm
(c)
(2³⁰ – 71)/7 gm
(d)
(2³⁰ + 71)/7 gm

9. PE 3 - Progressions | Algebra - Progressions

The 288^th term of the sequence a, b, b, c, c, c, d, d, d, d… is

(a)
u
(b)
v
(c)
w
(d)
x

10. PE 3 - Progressions | Algebra - Progressions

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

(a)
-2
(b)
-4
(c)
-12
(d)
8

PE 3 - Progressions | Algebra - Progressions

Feedback