*Watch the seventh video session on “Arithmetic Progressions” for Class X*^{th} – concepts and solved questions.

^{th}– concepts and solved questions.

**Arithmetic Progressions – Class X – Part 7 | Sum of first n terms (AP) | Exercise 5.3 | Q14-20 Solved**

Topics discussed:

Sum of first n terms of an AP: Expression for some derived:

S = (n/2) [ 2a + (n-1)d ]

S = (n/2) [ first term + last term ] = (n/2) [ a + l ]

Where a = first term, d = common terms, n = number of terms of the given AP, S = Sum of first n terms, l = a+(n-1)d = last term.

**Exercise 5.3 | Q14-20 Solved Completely with easy explanation**

14. Find the sum of the odd numbers between 0 and 50.

15. A contract on 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 the contractor has to pay as penalty, if he has delayed the work by 30 days?

16. 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.

17. 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 section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

18. 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, . . . as shown in Fig. 5.4 (refer to the image in video). What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take π =22/7 )

19. 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 (refer to the image in video). In how may rows are the 200 logs placed and how many logs are in the top row?

20. 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 straight line. There are ten potatoes in the line (refer to the image in video).A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

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