NCERT Solutions
Class 10 - Mathematics - Chapter 5: ARITHMETIC PROGRESSIONS

Exercise 5.3

Find the sum of the following APs:

1. 2, 7, 12, …, to 10 terms.
2. −37, −33, −29, …, to 12 terms.
3. 0.6, 1.7, 2.8, …, to 100 terms.
4. \(\dfrac{1}{15}\), \(\dfrac{1}{12}\), \(\dfrac{1}{10}\), …, to 11 terms.

Find the sums given below:

1. 7 + 10\(\dfrac{1}{2}\) + 14 + … + 84
2. 34 + 32 + 30 + … + 10
3. −5 + (−8) + (−11) + … + (−230)

In an AP:

1. given \(a = 5\), \(d = 3\), \(a_n = 50\), find \(n\) and \(S_n\).
2. given \(a = 7\), \(a_{13} = 35\), find \(d\) and \(S_{13}\).
3. given \(a_{12} = 37\), \(d = 3\), find \(a\) and \(S_{12}\).
4. given \(a_3 = 15\), \(S_{10} = 125\), find \(d\) and \(a_{10}\).
5. given \(d = 5\), \(S_9 = 75\), find \(a\) and \(a_9\).
6. given \(a = 2\), \(d = 8\), \(S_n = 90\), find \(n\) and \(a_n\).
7. given \(a = 8\), \(a_n = 62\), \(S_n = 210\), find \(n\) and \(d\).
8. given \(a_n = 4\), \(d = 2\), \(S_n = -14\), find \(n\) and \(a\).
9. given \(a = 3\), \(n = 8\), \(S_n = 192\), find \(d\).
10. given \(l = 28\), \(S_n = 144\), and there are total 9 terms. Find \(a\).

How many terms of the AP \(9, 17, 25, \ldots\) 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 the 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 \(a_1, a_2, \ldots, a_n, \ldots\) form an AP where \(a_n\) is defined as below :

(i) \(a_n = 3 + 4n\)

(ii) \(a_n = 9 - 5n\)

Also find the sum of the first 15 terms in each case.

The sum of the first terms of an AP is given as:

\(S_1 = 3,\ S_2 = 4\). Find:

\(a_2 = S_2 - S_1\), \(S_3\), \(a_3 = S_3 - S_2\), \(a_{10} = S_{10} - S_9\), and \(a_n = S_n - S_{n-1}\).

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 a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money has the contractor to pay as penalty if he has delayed the work by 30 days?

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

In a school, students thought of planting trees to reduce air pollution. The number of trees planted by each class section is equal to the class number. There are three sections of each class from I to XII. How many trees were planted by the students?

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, ... . Find the total length of thirteen consecutive semicircles. (Take \(\pi = \frac{22}{7}\))

200 logs are stacked so that the bottom row contains 20 logs, the next contains 19, then 18, and so on. In how many rows are the 200 logs placed and how many logs are in the top row?

In a potato race, a bucket is placed at the starting point. The first potato is 5 m away, and each subsequent potato is 3 m apart in a straight line. There are ten potatoes. A competitor picks each potato one at a time, returns to the bucket, and continues. Find the total distance the competitor runs.