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 in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time. Ans: Let’s start from making a sequence of the air amount in the […]
arithmatic progression
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 km when the fare is Rs 15 for the first km and Rs. 8 for each additional km. Ans: Let’s first start making a sequence and then check if the sequence
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 of the A.P. Hence, also find the sum of its first 20 terms. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Ans: Let’s consider the first terms of AP is a
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 the first term and common difference of A.P. Also, find the sum of all the terms of the A.P. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Let’s consider the first
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 (mn+1). Ans: Let first term of the given AP = a Common difference of the given AP = d Then, …………….(I) …………….(ii) Subtracting equation (ii) from equation (ii),we get Putting
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 −1/𝑛) + (4 −2/𝑛) + (4 −3/𝑛) +….. can be re-arranged as: (4 + 4 + 4 + 4 + ….. up to 𝑛 terms ) – (1 + 2
Find the sum of 𝑛 terms of the series (4 −1/𝑛) + (4 −2/𝑛) + (4 −3/𝑛) +….. Read More »
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 decides to mark the numbers on each chair from 1. 2. 3……. If there are 26 students and each student is seated at alternate position in examination hall such that
In a school examination hall, the teacher makes students sit in such a way that Read More »
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. If each prize is Rs. 40 less than the preceding price, find the value of each of the prizes. Ans: It is given that each prize money is less than the
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: Let = First term of the given A.P. and = Common difference . Then, . Now, Hence Proved! Please do press “Heart”
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 (2m-1) : (2n-1). Ans: Let: First term of given A.P. = , Common difference = , Then, the sums of m and n terms are given by Then, Please do