Arithmetic Progressions quiz

The common difference of the AP 3, 1, -1, -3, ... is:

The 11th term of the AP -3, -1/2, 2, ... is:

The 30th term of the AP 10, 7, 4, ... is:

The sum of the first 100 natural numbers is:

If 2x, x + 10 and 3x + 2 are three consecutive terms of an AP, the value of x is:

Which of the following is NOT an AP?

The number of terms in the AP 7, 13, 19, ..., 205 is:

The sum of the first n odd natural numbers is:

If the nth term of an AP is 3 + 4n, its common difference is:

In an AP, if a = 5, d = 3 and a_n = 50, then n is:

Is 301 a term of the AP 5, 11, 17, 23, ...? Justify your answer. (2 marks)

Find the 10th term from the last term of the AP 4, 9, 14, ..., 254. (2 marks)

Determine the AP whose third term is 16 and whose 7th term exceeds the 5th term by 12. (2 marks)

Find the sum of the odd numbers between 0 and 50. (2 marks)

Find the sum of the first 40 positive integers divisible by 6. (2 marks)

If the sum of the first n terms of an AP is S_n = 4n - n^2, find the first term and the common difference. (2 marks)

Show that a_n = 3 + 4n defines an AP and find the sum of its first 15 terms. (2 marks)

Find the sum 34 + 32 + 30 + ... + 10. (2 marks)

Two APs have the same common difference. The difference between their 100th terms is 100. What is the difference between their 1000th terms? Give a reason. (2 marks)

Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by Rs 1.75. In which week will her weekly savings be Rs 20.75? (2 marks)

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes. (3 marks)

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that production increases uniformly by a fixed number every year, find (i) the production in the first year (ii) the production in the 10th year (iii) the total production in the first 7 years. (3 marks)

A contract on construction work specifies a penalty for delay beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, and so on. How much money does the contractor have to pay as penalty if he delays the work by 30 days? (3 marks)

The first and last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum? (3 marks)

An auditorium has 20 seats in the first row, 22 seats in the second row, 24 seats in the third row, and so on, with 30 rows in all. Find the number of seats in the last row and the total number of seats in the auditorium. (3 marks)

Read the passage and answer the questions. In a school garden, students planted saplings in rows. The first row had 5 saplings, the second row had 8, the third row had 11, and so on, each row having 3 more saplings than the previous row. There are 15 rows in all. (i) Show that the numbers of saplings in the rows form an AP and write its first term and common difference. (ii) Find the number of saplings in the 15th row. (iii) Find the total number of saplings planted in the garden. (5 marks)

Read the passage and answer the questions. A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. The top and the bottom rungs are 2.5 m apart. (i) How many rungs does the ladder have? (ii) Show that the lengths of the rungs form an AP and find its common difference. (iii) Find the total length of wood required for the rungs. (5 marks)

Read the passage and answer the questions. Priya opens a recurring savings plan. She deposits Rs 1000 in the first month, Rs 1100 in the second month, Rs 1200 in the third month and continues to increase her deposit by Rs 100 every month. (i) How much will she deposit in the 12th month? (ii) In which month will her deposit be Rs 3000? (iii) What is the total amount she deposits in the first year? (5 marks)

Read the passage and answer the questions. A taxi charges Rs 50 for the first kilometre and Rs 15 for each additional kilometre. Riya notes the fare for 1 km, 2 km, 3 km and so on. (i) Write the first four fares and show that they form an AP. (ii) Write an expression for the fare for n km. (iii) Find the distance travelled if the fare paid was Rs 290. (5 marks)

Read the passage and answer the questions. In a class test, a teacher arranges marks for a series of problems so that the first problem carries 2 marks and each subsequent problem carries 2 marks more than the previous one. The total marks for the test is 110. (i) Write the AP formed by the marks of the problems. (ii) Form an equation in n for the total marks. (iii) Find the number of problems in the test and the marks of the last problem. (5 marks)

Derive the formula for the sum of the first n terms of an AP, S_n = (n/2)[2a + (n - 1)d], by writing the sum in the usual order and in reverse order and adding. Hence show that S_n = (n/2)(a + l), where l is the last term, and use it to find the sum of all three-digit natural numbers that are multiples of 7. (6 marks)

The 17th term of an AP exceeds its 10th term by 7. Find the common difference. If the first term is 3, find the 25th term and the sum of the first 25 terms. Plot the first five terms as points (n, a_n) on a graph and comment on the pattern formed by the points. (6 marks)

Draw a rough diagram of a staircase-like arrangement in which 1 block is in the top row, 2 in the next, 3 in the next, and so on. If the arrangement has 20 rows, find the number of blocks in the bottom row and the total number of blocks. If 210 blocks are available, how many complete rows can be made? (6 marks)

A spiral is made up of successive semicircles with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... Draw the first four semicircles. Show that their lengths form an AP, write its first term and common difference, and find the total length of a spiral made up of 13 consecutive semicircles. (Use pi = 22/7) (6 marks)

In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees each section of each class would plant would be the same as the class in which they are studying; for example, a section of Class I would plant 1 tree, a section of Class II would plant 2 trees, and so on till Class XII. There are three sections of each class. Show that the numbers of trees planted by the classes form an AP and find the total number of trees planted by the students. Draw a simple bar diagram showing the trees planted by Classes I to IV. (6 marks)