Arithmetic Progressions

Important Questions

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…

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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…

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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…

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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…

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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…

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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.…

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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:…

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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…

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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…

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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…

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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…

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

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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…

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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.…

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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…

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

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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…

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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…

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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…

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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.…

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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…

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

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Q) How many terms of the arithmetic progression 45, 39, 33, …….. must be taken so that their sum is 180? Explain the double answer.…

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Q) 250 logs are stacked in the following manner: 22 logs in the bottom row, 21 in the next row, 20 in the row next to…

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Q) The ratio of the 11th term to 17th term of an A.P. is 3:4. Find the ratio of 5th term to 21st term of the same…

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