In a flower bed, there are 43 rose plants in the first row, 41 in the second, 39 in the third, and so on.
Question:

In a flower bed, there are 43 rose plants in the first row, 41 in the second, 39 in the third, and so on. There are 11 rose plants in the last row. How many rows are there in the flower bed?

Solution:

The numbers of rose plants in consecutive rows are 43, 41, 39,…, 11.

Difference of rose plants between two consecutive rows = (41 – 43) = (39 – 41) = -2  [Constant]
So, the given progression is an AP.
Here, first term = 43
Common difference = -2
Last term = 11
Let n be the last term, then we have:
Tn = a + (n – 1)d
⇒ 11 = 43 + (n – 1)(-2)
⇒ 11 = 45 – 2n
⇒ 34 = 2n
⇒ n = 17
Hence, the 17th term is 11 or there are 17 rows in the flower bed.
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