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Example 3: 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?

Solution : The number of rose plants in the 1st, 2nd, 3rd, . . ., rows are :

23, 21, 19, . . ., 5

It forms an AP.

Let the number of rows in the flower bed be n.

Then a = 23, d = 21 – 23 = – 2, a n = 5

As, a n = a + (n – 1) d

We have, 5 = 23 + (n – 1)(– 2)

i.e., – 18 = (n – 1)(– 2)

i.e., n = 10

So, there are 10 rows in the flower bed.

Key Concepts-

 AN AP is a list of number in which difference of a term and the preceding term is
always constant. The constant is called common difference (d) of AP. d=a n+1-a n
 If a is the first term and ‘d’ is the common difference of an AP, then the AP is a,
a+d, a+2d, a+3d…..
 The nth term of an AP is denoted by a n
a n=a+(n-1)d
where a = first term
d= common difference
n= number of term
 nth term from the end = l - (n -1)d
where l = last term
 Various terms in an AP can be chosen in following manner.

No. of Terms Terms Common Difference
3 a-d, a, a+d d
4 a-3d, a-d, a+d, a+3d 2d
5 a-2d, a-d, a, a+d, a+2d d

Example 4-

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