A.P. and G.P.

A story is written such that the sum of 25 chapters on each continuous page makes up a grand total of 1200 pages. What is the number of pages in the first chapter if each chapter increases by one unit number of pages?

1. 36
2. 45
3. 40
4. 55

Answer: (a) 36

In a geometric sequence, the first term is 8 and the common ratio is 0.5. Determine the term number n for which the nth term is 1.

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

Answer: (a) 4

The sum of first four terms of geometric progression (G.P.) is 65/12 and the sum of their respective reciprocals is 65/18. If the product of first three terms of the G.P. is 1, and the third term is α, then 2α is

1. 8
2. 4
3. 5
4. 3

Answer: (d) 3

Which of the following matches is correct? Column A Column B 1 Temperatures decreasing by 1°C each hour. a Arithmetic Sequence 2 Interest compounding annually in a savings account. b Geometric Sequence 3 A book series releasing one book per year. c Neither 4 A car accelerating by an additional 5 km/h each second.

1. 1 - a, 2 - b, 3 - a, 4 - a
2. 1 - a, 2 - b, 3 - c, 4 - a
3. 1 - c, 2 - a, 3 - b, 4 - a
4. 1 - a, 2 - a, 3 - b, 4 - b

Answer: (a) 1 - a, 2 - b, 3 - a, 4 - a

The ratio between the sum of the first n terms of two arithmetic progressions (A.P.) is given as p(n) = {3n + 9} : {7n + 15}. Find the ratio between their 12th term.

1. 4 : 7
2. 21 : 45
3. 39 : 88
4. 12 : 17

Answer: (c) 39 : 88

Find the sum of the following sequence: 12, 132, 1332, 13332, ......... to n terms.

1. 120(10n - 1)/81
2. 120(10n)/9 - 12n/81
3. 120/81(10n - 1) - n/9
4. 120/81(10n - 1) - (12n/9)

Answer: (d) 120/81(10n - 1) - (12n/9)

Consider a cultural exhibit where the number of visitors decreases by half every subsequent decade, starting from 1024 visitors in the year 2000. Determine the expected count of visitors in the year 2040, if the trend continues.

1. 128 visitors
2. 64 visitors
3. 12 visitors
4. 80 visitors

Answer: (b) 64 visitors

ak is a sequence of integers, with a1 = -2 and a(m + n) = am + an + mn, for all positive integers m, n. What is the value of a8?

1. 16
2. 18
3. 12
4. 10

Answer: (c) 12

The sum of an infinite G. P. with positive terms is 48 and sum of its first two terms is 36. Find the second term.

1. 15
2. 10
3. 12
4. 5

Answer: (c) 12

A car travels around a circular track circumference of 400 m. Every minute, it increases its speed such that the distance covered in the nth minute forms an arithmetic sequence. If the car covers 120 m in the first minute and 140 m in the second minute, how many complete rounds does the car take in the first 10 minutes?

1. 3
2. 5
3. 10
4. 8

Answer: (b) 5