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 that the sum of its first (m + n) terms is zero. Ans: Step 1: We know that the sum of first m terms of an AP is given by: Sm […]
arithmatic progression
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 1: Let’s consider that the middle term is A, first term is A – D and third term is A + D, here D is the common difference. By given 1st
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: Since we need to find out numbers divisible by 4 between 10 and 300. These numbers will be in an AP where common difference will be 4. Let’s find out
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 last term. Since we need to find out numbers divisible by 7 between 50 and 500. These numbers will be in an AP where common difference will be 7. 1st
Find the sum of all integers between 50 and 500, which are divisible by 7. Read More »
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 used at landfills or in agriculture. A company started making road rollers 10 years ago and increased its production uniformly by a fixed number every year. The company produces 800
A road roller is a compactor-type engineering vehicle, Read More »
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, – 1/2, – 1/2, – 1/2, … Ans: Here we are given a sequence and we need to determine if the sequence qualifies to be an AP or not. After
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, 0.222, 0.2222, … Ans: Here we are given a sequence and we need to determine if the sequence qualifies to be an AP or not. After that, we need to
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 + √2, 3 + 2√2, 3 + 3√2, … Ans: Here we are given a sequence and we need to determine if the sequence qualifies to be an AP or
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, – 3.2, – 5.2, – 7.2, … Ans: Here we are given a sequence and we need to determine if the sequence qualifies to be an AP or not. After
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 ,3, 7/2, … Ans: Here we are given a sequence and we need to determine if the sequence qualifies to be an AP or not. After that, we need to