48 solutions available
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...
For the following APs, write the first term and the common difference: (i) 3, 1, -1, -3, …… (ii) -5, -1, 3, 7, …… (iii) \(\frac { 1 }{ 3 }\) ,...
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. (i) 2, 4, 8, 16, ……. (ii) 2, \(\frac {...
Write first four terms of the AP, when the first term a and the common difference d are given as follows: (i) a = 10, d = 10 (ii) a = -2, d = 0 (iii)...
Fill in the blanks in the following table, given that a is the first term, d the common difference and the nth term of the AP:
In the following APs, find the missing terms in the boxes:
Which term of the AP: 3, 8, 13, 18, …, is 78?
Find the number of terms in each of the following APs: (i) 7, 13, 19, …, 205 (ii) 18, 15\(\frac { 1 }{ 2 }\), 13, …, -47
Check, whether -150 is a term of the AP: 11, 8, 5, 2, ….
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
If the 3rd and the 9th term of an AP are 4 and -8 respectively, which term of this AP is zero?
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
How many three-digit numbers are divisible by 7?
How many multiples of 4 lie between 10 and 250?
For what value of n, the nth term of two APs: 63, 65, 61,… and 3, 10, 17,… are equal?
Determine the AP whose 3rd term is 16 and 7th term exceeds the 5th term by 12.
Find the 20th term from the last term of the AP: 3, 8, 13, …, 253.
Which term of the AP: 3, 15, 27, 39, … will be 132 more than its 54th term?
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000 ?
Ramkali saved ₹ 5 in the first week of a year and then increased her weekly saving by ₹ 1.75. If in the nth week, her weekly saving become ₹ 20.75,...
Find the sum of the following APs: (i) 2, 7, 12,…… to 10 terms. (ii) -37, -33, -29, …… to 12 terms. (iii) 0.6, 1.7, 2.8, ……, to 100 terms. (iv)...
Find the sums given below: (i) 7 + 10\(\frac { 1 }{ 2 }\) + 14 + … + 84 (ii) 34 + 32 + 30 + … + 10 (iii) -5 + (-8) + (-11) + ….. + (-230)
In an AP: (i) given a = 5, d = 3, an = 50, find n and Sn. (ii) given a = 7, a13 = 35, find d and S13. (iii) given a12 = 37, d = 3, find a and S12....
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.
Show that a1, a2, ……. an,…… form an AP where an is defined as below: (i) an = 3 + 4n (ii) an = 9 – 5n Also find the sum of the first 15 terms in each...
Find the sum of the odd numbers between 0 and 50.
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the...
A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less...
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, that each...
200 logs are stacked in the following manner 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Figure). In how...
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a...
How many terms of AP: 9, 17, 25, … must be taken to give a sum of 636?
The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
The first and the 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?
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
If the sum of the first n terms of an AP is 4n – n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second...
Find the sum of the first 40 positive integers divisible by 6.
Find the sum of the first 15 multiples of 8.
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...
The sum of the third term and the seventh term of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP?
Which term of the AP: 121, 117. 113, ….., is its first negative term?
A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 at the top. If the top and the bottom rungs are...
The houses of a row are numbered consecutively from 1 to 49. Show that there is value of x such that the sum of the numbers of the houses preceding...
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of \(\frac {...
