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Arithmetic Progressions
Question
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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 plant in the last row. How many rows are there in the flower bed?

Answer

The number of rose plants in the rows are 23, 21, 19, .......... 5
Here, a = 23, d = –2, an = 5
We know that,an = a + (n – 1)d
⇒ 5 = 23 + (n – 1) (–2)
⇒ 5 = 23 – 2n + 2
⇒ 5 = 25 – 2n
⇒ 2n = –20
⇒ n = 10
Hence, there are 10 rows in the flower bed.

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Some More Questions From Arithmetic Progressions Chapter

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

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In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a – 10, d = 10

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = –2, d = 0

Write first four terms of the AP, when the first term a and the common difference d are given as follows:
a = 4, d = – 3

Write first four terms of the AP, when the first term a and the common difference d are given as follows:

a = – 1.25, d = – 0.25