Question

Arithmetic progression is sequence of numbers such that the difference of any two successive members of the sequence is a constant.



Reema being plant lover decides to open a nursery and she bought few plants with pots. She wants to place pots in such a way that number of pots in first row is 3, in second row is 5 and in third row is 7 and so on.



(a) If Reema wants to place 120 pots in total then the total number of rows formed in this arrangement is

(i) 12 (ii) 10 (iii) 14 (iv) 8

(b) How many pots are placed in last row?

(i) 22 (ii) 21 (iii) 24 (iv) 18



(c) Find the difference in number of pots placed in 8th row and 3rd row?

(i) 10 (ii) 11 (iii) 14 (iv) 15



(d) If Reema has sufficient space for 15 rows then how many total number of pots are placed by her with same arrangement?

(i) 200 (ii) 150 (iii) 255 (iv) 180



(e) If for an AP an = 4n + 5 find the common difference

(i) 5 (ii) 4 (iii) 1 (iv) 0​

Answer 1

Given : Reema wants to place pots in such a way that number of pots in first row is 3, in second row is 5 and in third row is 7 and so on.

Reema wants to place 120 pots in total

To Find : total number of rows formed in this arrangement

How many pots are placed in last row?

difference in number of pots placed in 8th row and 3rd row

Solution:

AP

3 , 5 , 7 , ..........

a = 3

d = 2

rows = n

=> (n/2) (2*3 + (n-1)2)  = 120

=> n(n+ 2) = 120

=> n = 10

10 Rows

Last row is 10th

= 3 + (10 - 1)2

= 3 + 18

= 21

difference in number of pots placed in 8th row and 3rd row

= 5(2) = 10

15 rows

(15/2)(2*3 + 14*2)

= 15*17

= 255

an = 4n + 5

common difference = 4

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