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Answer 1

Question:-

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?

Answer :-

Given :-

• In flower bed.
• There are 23 rose in first row.
• There are 21 in second row.
• 19 in third row.
• In last row there is 5 rose plants.

To find :-

• Number of rows.

We know that it follows the sequence of 23, 21, 19 ---------- 5. So here is the question of Arithmetic Progression.

We know that,

• Sequence:- 23, 21 , 19 , - - - - - - - - - - - 5.

• Common differences
• = Second term - First term
• = 21 - 23 = -2 & also :-
• = 19 - 21 = -2

So,

First term = a = 23

Common difference = d = -2

$\mathtt{Last \: term = l = a_n = 5 }</p><p>$

Formula applies on it is :-

${\boxed{\orange{\Large{\mathtt{\leadsto{a_n = a +(n-1) d}}}}}}$

So,Number of flower bed is :-

${\mathtt{\implies{5 = 23 + (n - 1) - 2}}}$

${\mathtt{\implies{5 - 23 = (n - 1) - 2}}}$

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

$\\ {\mathtt{\implies{ \frac{ - 18}{ - 2} = n - 1}}}$

${\mathtt{\implies{n - 1 = 9}}}$

${\mathtt{\implies{n = 9 + 1}}}$

$\large{ \color{green}{\mathtt{\implies{n = 10}}}}$

No, of flower bed Is 10