problem archive
-
Find the sum of first 24 terms of the list of numbers whose nth term is given by \(a_n = 3 + 2n\) -
A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a ... -
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, a_n = 50, find n and S_n. (ii) given a = 7, a_3 = 35, find d and S_{13}. (iii) given a_{12} = 37, d = 3, find a and ... -
How many terms of the 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 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 e... -
If the sum of the first n terms of an AP is 4n - n^2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term... -
Find the sum of the first 40 positive integers divisible by 6. -
Find the sum of the first 15 multiples of 8. -
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 se... -
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 than... -
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 s... -
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 cm...