Competency Based Questions Chapter 5 Arithmetic Progressions

Hint: Produce patterns in order to observe than succeeding terms are obtained by adding a fixed number to the preceding terms.

Question.1. What are the missing numbers in the pattern given below?
-32, -19.5, -7, ___, 18, 30.5, _____

(a) 19.5 and 43
(b) 5.5 and 43
(c) 5 and 43
(d) 5 and 43.5

Question.2. Which of the following two numbers do you think should be the succeeding terms of the pattern below?
\frac{-1}{3}, \frac{-1}{12}, \frac{1}{6}, \frac{5}{12}, __, __

(a) \frac{2}{3} and \frac{11}{12}
(b) \frac{4}{6} and \frac{11}{4}
(c) \frac{4}{6} and \frac{12}{11}
(d) \frac{1}{2} and \frac{24}{22}

Ans.1. (b) 5.5 and 43
Ans.2. (a) \frac{2}{3} and \frac{11}{12}

Hint: Distinguish between finite and infinite AP in order to determine the nature and write the last term of the given AP.

Question.3. Which of the following is an infinite AP?

(i) -2, -1, 0, 1, 2, 3, 4, 5, 6, 7…
(ii) -14, -12, -10, -8, ___, ____, ____, 0
(iii) First 40 even numbers
(iv) Odd Numbers

(a) (i) and (ii)
(b) (ii) and (iii)
(c) (i) and (iv)
(d) (ii) and (iv)

Question.4. What would be the last term of an arithmetic progression with 10 terms whose second term is -23 and the third term is -35?

(a) 119
(b) -107
(c) -650
(d) -12

Ans.3. (c) (i) and (iv)
Ans.4. (a) 119

Hint: Calculate the n^{th} term of a given AP in order to find its terms and their nature.

Question.5. If the first term of an AP is 2 and the common difference is \frac{-1}{2}, what would be the 12^{th} term of the AP?

(a) 2 + 11 \left(\frac{-1}{2}\right)
(b) 2 + 12 \left(\frac{-1}{2}\right)
(c) 2 − 11 \left(\frac{-1}{2}\right)
(d) 2 − 12 \left(\frac{-1}{2}\right)

Question.6. Find the n^{th} term of the AP shown below.
_, _, -36, _, – 44, ………. up to n

(a) 4n – 32
(b) -40 + 4n
(c) 24 – 4n
(d) – 4n – 24

Ans.5. (a) 2 + 11 \left(\frac{-1}{2}\right)
Ans.6. (d) – 4n – 24

Hint: Calculate the n^{th} term of a given AP in order to solve for a real-life word problem.

Question.7. Jessie needs ₹1,70,000 for her College admissions in the starting of January 2021. Her mother helped her by creating a fund of ₹12,000 in the end of January 2019. Thereafter she has been collecting ₹5500 in the starting of each month for Jessie’s college fund. How much money will be collected in the fund before Jessie’s admissions?

(a) ₹(12000 + 11(5500))
(b) ₹(5500 + 11(12000))
(c) ₹(12000 + 23(5500))
(d) ₹(5500 + 23(12000))

Question.8. On an average Jane writes 12 short stories every year. Although in the first year she was able to write some more short stories. If after 12 years of her career she has written a total of 147 stories. How many had she written after 7 years of her writing?

(a) 75
(b) 84
(c) 87
(d) 90

Ans.7. (c) ₹(12000 + 23(5500))
Ans.8. (c) 87

Hint: Calculate the sum of a given AP in order to get the solution for a real-life word problem.

Question.9. Aamod loves to travel and he travels every year. He has seen 8 different cities in his first year. Thereafter every year he has seen 2 cities. If he had followed this pattern, how many cities did he see by the end of 10 years of travel?

(a) [5{16 + 9(2)}] cities
(b) [5{8 + 9(2)}] cities
(c) [5{16 + 10(2)}] cities
(d) [5{8 + 10(2)}] cities

Question.10. Mr. Kapoor is collecting donations for building a new school building in a village. His wife starts by donating ₹125000. His brother also contributes by donating ₹54000. Thereafter every person who contributes in the donation pays ₹5250 more than the previous donor. How much amount has Mr. Kapoor able to collect after 23 donations?

(a) ₹164250
(b) ₹2400750
(c) ₹2525750
(d) ₹2570250

Ans.9. (a) [5{16 + 9(2)}] cities

Hint: Calculate the sum of a given AP in order to solve for various questions related to progression.

Question.11. What is the sum of all the three-digit numbers divisible by 12?

(a) \left[\frac{73}{2} \left(108+996\right) \right]
(b) \left[\frac{75}{2} \left(216+996\right) \right]
(c) \left[\frac{73}{2} \left(216+996\right) \right]
(d) \left[\frac{75}{2} \left(108+996\right) \right]

Question.12. The sum of first 76 terms of an AP is 21850 and the sum of first 40 terms is 7900. Find the sum of first 100 terms of this AP

(a) 29750
(b) 34155
(c) 34750
(d) 35350

Ans.11. (d) \left[\frac{75}{2} \left(108+996\right) \right]
Ans.12. (c) 34750

Hint: Calculate the last term of the given AP in order to find the solution for a real-life word problem.

Question.13. Mr. Singh buys a property every year for 12 years. Every year he buys x acres more than the previous year. If in the 8^{th} year he bought 45 acres of land and in the 5^{th} year he bought 30 acres of land, how many acres did he buy in the last year?

(a) \left[10+11\left(5\right)\right] Acres
(b) \left[10+11\left(5\right)\right] Acres
(c) \left[10+11\left(5\right)\right] Acres
(d) \left[10+11\left(5\right)\right] Acres

Question.14. Ranvijay likes to collect stamps. He has a total of 4290 stamps after 10 years of his stamp collection. He counted his total stamps in the 6^{th} year as well and found that he had a total of 1830 stamps then. How many stamps did he collect in the last year of his collection?

(a) 522
(b) 646
(c) 708
(d) 1370

Ans.13. (a) \left[10+11\left(5\right)\right] Acres
Ans.14. (c) 708

Hint: Use appropriate formula to calculate the last term of the given AP.

Question.15. The first term of an AP is -76 and the sum of first 45 terms is -9360. Which of the following is the last term of this AP?

(a) 416+76
(b) 416-76
(c) -416-76
(d) -416+76

Question.16. The sum of n terms of an AP is 8558. If the 15^{th} term is 97 and the 10^{th} term is 32. What is the n^{th} term?

(a) 431
(b) 474
(c) 644
(d) 7612

Ans.15. (d) -416+76
Ans.16. (b) 474

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