## Arithmetic Progressions

### Important Questions

Q) If the sum of first m terms of an A.P. is same as sum of its first n terms (m ≠ n), then show…

Q) In an A.P., the sum of three consecutive terms is 24 and the sum of their squares is 194. Find the numbers. Ans:  Step…

Q) How many numbers lie between 10 and 300, which when divided by 4 leave a remainder 3? Also find their sum? Ans:  Step 1:…

Q) Find the sum of all integers between 50 and 500, which are divisible by 7. Ans:  Step 1: Let’s find out 1st term and…

Q) A road roller is a compactor-type engineering vehicle, used to compact soil, gravel, concrete, etc, in the construction of roads and foundations. They are also…

Q) February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. Some people in India also started celebrating…

Q) Which of the following are APs? If they form an AP, find the common difference d and write three more terms.  (viii) – 1/2,…

Q) Which of the following are APs? If they form an AP, find the common difference d and write three more terms.  (vi) 0.2, 0.22,…

Q) Which of the following are APs? If they form an AP, find the common difference d and write three more terms.  v) 3, 3…

Q) Which of the following are APs? If they form an AP, find the common difference d and write three more terms.  iii) – 1.2,…

Q) Which of the following are APs? If they form an AP, find the common difference d and write three more terms. (ii) 2, 5/2…

Q) For the following APs, write the first term and the common difference: (iv) 0.6, 1.7, 2.8, 3.9,… Ans: Here we are given AP and…

Q) For the following APs, write the first term and the common difference: (iii) ,…. Ans: Here we are given AP and we need to…

Q) For the following APs, write the first term and the common difference: (ii) – 5, – 1, 3, 7…. Ans: Here we are given…

Q) Write first four terms of the A.P. when the first term a and the common difference d are given as follows (v) a =…

Q) Write first four terms of the A.P. when the first term a and the common difference d are given as follows (iv) a =…

Q) Write first four terms of the A.P. when the first term a and the common difference d are given as follows (iii) a =…

Q) In which of the following situations does the list of numbers involved make an arithmetic progression and why? (iv) The amount of money in…

Q) In which of the following situations does the list of numbers involved make an arithmetic progression and why? (iii) The cost of digging a…

Q) In which of the following situations does the list of numbers involved make an arithmetic progression and why? (ii) The amount of air present…

Q) In which of the following situations does the list of numbers involved make an arithmetic progression and why? (i) The taxi fare after each…

Q) The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference…

Q) In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine…

Q) If the mth term of an AP is 1/n and the nth term is 1/m, then show that the sum of (mn)th term is…

Q) Find the sum of 𝑛 terms of the series (4 −1/𝑛) + (4 −2/𝑛) + (4 −3/𝑛) +….. Ans:  Method 1: The AP (4…

Q) In a school examination hall, the teacher makes students sit in such a way that no students can cheat from other student. So, the teacher…

Q) A sum of Rs. 1400 is to be used to give seven cash prizes to students of a school for their overall academic performance.…

Q)  If the sum of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m+n) terms is zero. Ans:…

Q)  The ratio of the sum of m and n terms of an A.P. is . Show that the ratio mth and nth term is…

Q)   In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate…

Q)   Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of…

Q)   Find the common difference of an A.P. whose first term is 8, the last term is 65 and the sum of all its terms…

Q)   In an AP, the sum of the first n terms is given by Sn = 6n – n2. Find its 30th term. Ans: We…

Q)  Deepa has to buy a scooty. She can buy scooty either making cashdown payment of ₹ 25,000 or by making 15 monthly instalments as…

Q)   India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs.…

Q)  Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86m at the Asian Grand Prix in 2017…

Q) If pth term of an A.P. is q and qth term is p, then prove that its nth term is (p + q –…

Q) Rohan repays his total loan of Rs.1,18,000 by paying every month starting with the first installment of Rs. 1,000. If he increases the installment…

Q) The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term. Ans: Given that…

Q) Which term of the A.P. : 65, 61, 57, 53,………… is the first negative term. Ans: This is A.P. of decreasing order. In the…

Q) How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively and the last term is 62.…

Q) Prerna saves Rs. 32 during the first, month, Rs. 36 in the second month and Rs. 40 in the third month. if she continues…

Q)  Solve the equation for x: 1 + 4 + 7 + 10 + …. + x = 287 Ans:  We can see that it…