# NCERT Mathematics Class 10 Exemplar Ch 5 Arithmetic Progressions Part 3 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**EXERCISE 5.2**

1. Which of the following form an AP? Justify your answer.

(i) (ii)

(iii) (iv)

(v) (vi)

(vii)

Answer: (i) , (iv) and (vii) form an AP as in each of these 1 – k, k, a, a is the same for different values of k.

2. Justify whether it is true to say that forms an AP as .

Answer: False, as

3. For the AP: can we find directly without actually finding ? Give reasons for your answer.

Answer: Yes,

4. Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10^{th} terms is the same as the difference between their 21^{st} terms, which is the same as the difference between any two corresponding terms. Why?

Answer: The difference between any two corresponding terms of such APs is the same as the difference between their first terms.

Is 0 a term of the Justify your answer.

Answer: No.

6. The taxi fare after each km, when the fare is ₹ 15 for the first km and ₹ 8 for each additional km, does not form an AP as the total fare (in ₹) after each km is Is the statement true? Give reasons.

Answer: No, as the total fare (in ₹) after each km is

7. In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

(i) The fee charged from a student every month by a school for the whole session, when the monthly fee is ₹ 400.

(ii) The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is ₹ 250, and it increases by ₹ 50 for the next higher class.

(iii) The amount of money in the account of Varun at the end of every year when ₹ 1000 is deposited at simple interest of 10 % per annum.

(iv) The number of bacteria in a certain food item after each second, when they double in every second.

Answer: (i) , (ii) and (iii) form an AP as in the list of numbers formed every succeeding term is obtained by adding a fixed number.

8. Justify whether it is true to say that the following are the nth terms of an AP.

(i) (ii) (iii)

Answer: (i) Yes (ii) No (iii) No