CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set B

Arithmetic Progression MCQ Questions with Answers Class 10 

Assertion Reasoning Questions Arithmetic Progression

Directions:
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : If S_n is the sum of the first n terms of an A.P., then its nth term an is given by an = S_n – S_n – 1 .
Reason : The 10^th term of the A.P. 5, 8, 11, 14, ………………. is 35.
Answer : C

Question. Assertion: arithmetic mean between 5 and 90 is 47.5
Reason: arithmetic mean between two given number a,b is (a+b)/2
Answer : A

Question. Assertion: the value of n, if a = 10, d = 5, an = 95.
Reason: the formula of general term an is an= a+(n-1)d.
Answer : A

Question. Assertion: The constant difference between any two terms of an AP is commonly known as common difference
Reason: the common difference of 2,4,6,8 this A.P. sequence is 2
Answer : A

Question. Assertion : Let the positive numbers a, b, c be in A.P., then 1/bc, 1/ac, 1/ab are also in A.P.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
Answer : A

CASE STUDY QUESTIONS

Q1. Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month , answer the following:

Question. Find the amount paid by him in 30th installment.
Answer : 3900

Question. Find the amount paid by him in the 30 installments.
Answer : 73500

Question. If total instalments are 40 then amount paid in the last installment?
Answer : 490

Q2. 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 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?

Question. Find terms of AP formed in above situation
Answer : 10, 16 , 22……..

Question. What is the total distance the competitor has to run?
Answer : Total distance 370

Question. Find distance cover after 4 potato drop In the bucket?
Answer : 152 m

Very Short Answer Type Questions

Question. Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Answer : No

Question. 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 second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 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?
Answer : Rs 27750

Question. Find the 31^st term of an AP whose 11th term is 38 and the 16^th term is 73.
Answer : 178

Question. Find the 20^th term from the last term of the AP : 3, 8, 13, . . ., 253
Answer : 20^th term from the last term is 158

Question. In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on.
There are 5 rose plants in the last row. How many rows are there in the flower bed?
Answer : 10 rows

Question. For the AP : 1/3, 5/3, 9/3, 13/3,....... write the first term a and the common difference d.
Answer : a = 1/3, d= 4/3

Question. The 17^th term of an AP exceeds its 10th term by 7. Find the common difference.
Answer : 1

Question. 200 logs are stacked in following manner . 20 logs in the bottom row , 19 in the next row 18 in the row next to it and so on . how many rows are the 200 logs placed and how many logs are in the top row ?
Answer : total rows 16 and 5 logs placed in top row

Question. Ramkali saves Rs 5 in the first week, of a year and increased her weekly savings by Rs 1.75. If in the nth week her weekly savings became Rs 20.75, find n.
Answer : 10

Question. The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.
Answer : 852

Question. The sum of the third and seventh terms of an A.P. is 40 and the sum of its sixth and 14th terms is 70. Find the sum of the first ten terms of the A.P.
Answer : 215

Question. If sum of first n terms of an AP is 4n – n² What is the first term What is the sum first two terms ?
Find 10th term , 3^rd term and nth term .
Answer : S1 = 3 S2 = 4 a₁₀= -15 a₃ = -1 and nth term = 5-2n

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