Question

in a garden bed there are 23 roses plants in the First row 21 are in the second row 19 in third row and so on there are 5 plans in the last row how many rows are there of the rose plants also find the total number of Rose plants in the garden

Answer 1

Here a=23 ; d= -2 and an=5

an = a + (n-1)d

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

-->5 = 23 +2 -2n

-->5 = 25 -2n

--> -2n = -20

-->n=10

Sn = n/2(a + an)

--> 10/2(23 + 5)

-->5 X 28

=140

-->There are 140 roses on the flower bed..

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

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The total number of rose plants in 1st , 2nd , 3rd .......... and last row are :-

23, 21, 19,...........,5

Let us assume that the number of rows of rose plants be n.

The sequence of an A.P :- 23, 21, 19,...........,5

Fist term ( a ) = 23

Common difference ( a₁ - a₂ ) = -2

nth term = 5.

Therefore using this formula :-

an = a+(n-1)d

5 = 23 + ( n - 1 ) × -2

5 = 23 - 2n + 2

20 = 2n

n = 10.

$\huge{\boxed{\sf{Hence\:there\:are\:10\:rows\:of\:rose\:plants\:.}}}$

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