# NCERT Mathematics Class 10 Exemplar Ch 5 Arithmetic Progressions Part 3

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

Answer: No, as the total fare (in Rs) 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 Rs 400.

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

(iii) The amount of money in the account of Varun at the end of every year when Rs 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