Progressions — Practice

Question 1

The minimum taxi fare is Rs 20 for the first km and Rs 8 for each additional km. Does the list of fares form an arithmetic progression? Give a reason.

Accepted Answer

Yes, it is an A.P. with a = 20 and d = 8

Question 2

A vacuum pump removes one quarter of the air remaining in a cylinder at each stroke. Does the amount of air left form an arithmetic progression?

Accepted Answer

No, it is a geometric progression, not an arithmetic one

Question 3

Which of these are A.P.s? If so, give the common difference and the next three terms. (a) 0, -4, -8, -12, ...  (b) 1, 3, 9, 27, ...  (c) root2, root8, root18, root32, ...

Accepted Answer

(a) A.P., d = -4, next -16, -20, -24;  (b) not an A.P.;  (c) A.P., d = root2, next root50, root72, root98

Question 4

Find the 30th term of the A.P. 10, 7, 4, ...

Accepted Answer

-77

Question 5

Check whether -150 is a term of the A.P. 11, 8, 5, 2, ...

Accepted Answer

No, it is not a term

Question 6

Find the 31st term of an A.P. whose 11th term is 38 and 16th term is 73.

Accepted Answer

178

Question 7

How many three-digit numbers are divisible by 7?

Accepted Answer

128

Question 8

Find the 20th term from the end of the A.P. 3, 8, 13, ..., 253.

Accepted Answer

158

Question 9

Subba Rao started his job in 1995 at a monthly salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his salary reach Rs 7000?

Accepted Answer

In 2005, which is the 11th year of his service

Question 10

Find the sum of the A.P. 2, 7, 12, ... to 10 terms.

Accepted Answer

245

Question 11

Find the sum 34 + 32 + 30 + ... + 10.

Accepted Answer

286

Question 12

If the sum of the first 7 terms of an A.P. is 49 and that of the first 17 terms is 289, find the sum of the first n terms.

Accepted Answer

Sₙ = n squared

Question 13

If the sum of the first n terms of an A.P. is 4n - n squared, find the first term, the second term, the third term, the tenth term and the nth term.

Accepted Answer

a1 = 3, a2 = 1, a3 = -1, a10 = -15, and aₙ = 5 - 2n

Question 14

A sum of Rs 700 is to be used for seven cash prizes, each prize Rs 20 less than the one before. Find the value of each prize.

Accepted Answer

Rs 160, 140, 120, 100, 80, 60 and 40

Question 15

200 logs are stacked with 20 logs in the bottom row, 19 in the row above, 18 above that and so on. In how many rows are the 200 logs placed, and how many logs are in the top row?

Accepted Answer

16 rows, with 5 logs in the top row

Question 16

A spiral is made of thirteen successive semicircles with centres alternating between two points, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and so on. Find the total length of the spiral, taking pi as 22/7.

Accepted Answer

143 cm

Question 17

Which of these are G.P.s? If so, write the next three terms. (a) 4, 8, 16, ...  (b) 5, 55, 555, ...  (c) 0.4, 0.04, 0.004, ...

Accepted Answer

(a) G.P., next 32, 64, 128;  (b) not a G.P.;  (c) G.P., next 0.0004, 0.00004, 0.000004

Question 18

Find x so that x, x + 2 and x + 6 are consecutive terms of a geometric progression.

Accepted Answer

x = 2

Question 19

For the geometric progression 5, 2, 4/5, 8/25, ... find the common ratio and the nth term.

Accepted Answer

r = 2/5 and aₙ = 5 times (2/5)^(n-1)

Question 20

Which term of the G.P. root3, 3, 3root3, ... is 729?

Accepted Answer

The 12th term

Question 21

The geometric progressions 162, 54, 18, ... and 2/81, 2/27, 2/9, ... have their nth terms equal. Find the value of n.

Accepted Answer

n = 5

Question 22

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding house x equals the sum of those following it, and find x.

Accepted Answer

x = 35

Question 23

Which of the following is an arithmetic progression? (a) 2, 3, 5, 7, 8, 10, 15  (b) 2, 5, 7, 10, 12, 15  (c) -1, -3, -5, -7  (d) 1, 1, 2, 3, 5

Accepted Answer

(c) -1, -3, -5, -7

Practice — Progressions

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