Question

In a flower bed there are 23 rose plants in the first row, 21 in second and so on. There are 5 rose plants in the last row. How many rows are there in flower bed?

Answer 1

In a flower bed there are 23 rose plants in the first row, 21 in second and so on. There are 5 rose plants in the last row. How many rows are there in flower bed?

Good question,

Here is your perfect answer!

This is an AP question,

Here first term (a) = 23,

d(common diff) = 21 - 23

= - 2,

There are 5 rose plants in last row,

Hence a(n) = 5

To find n(no of terms or rows),

Since a(n) = a + (n-1)d

General term's formula,

=) 5 = 23 + (n-1)*-2

=) 5-23 = (n-1)*-2

=) - 18/-2 = (n-1)

=) 9 = (n-1)

=) 9+1 = n

=) 10 = n

Hence no of rows in flower beds = 10.

Answer 2

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$\bf{QUESTION}$
In a flower bed there are 23 rose plants in the first row, 21 in second and so on. There are 5 rose plants in the last row. How many rows are there in flower bed?


$\bf{step \: by \: step \: explanation}$

THE NUMBER OF ROSE PLANT 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

$\bf{ = > -2}$
$\large{a \tiny \: n \large = 5}$

$\large \bf{ a \tiny \: n \large = a + (n - 1)d}$


$\bf{ = > 5 = 23 + (n - 1)( - 2)}$


$\bf{ - 18 = (n - 1)( - 2)}$

$\bf { - 2n + 2 = - 18} \\ \\ \bf{ - 2n = - 18 - 2} \\ \\ \bf{ - 2n = - 20}$


$\bf \huge{ n = 10}$


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