Question

A flower bed there are twenty three 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 1

$\boxed{\bold{\large{Answer:}}}$

$\text{Let\:the\:No.\:of\:Rows\:in\:flower\:bed\:be\:n}$

aₙ = 5

$\text{a\:=\:23}$

$\text{d\:=\:21\:-\:23\:=\:-2}$

$\text{We\:know\:that,}$

aₙ = a+(n-1)d

$\text{Executing\:in\:formula\:we\:get,}$

$\implies5 = 23 + (n - 1)( - 2) \\ \\ \implies5 = 23 - 2n + 2 \\ \\ \implies5 = 25 - 2n \\ \\ \implies2n = 25 - 5 \\ \\ \implies2n = 20 \\ \\ \implies \: n = \frac{20}{2} \\ \\ \implies \: n = 10$

$\text{Thus,\:there\:are\:10\:rows\:in\:flower\:bed.}$

$\boxed{\bold{\large{Hope\:it\:helps\:you!}}}$

Answer 2

The number of rose plants in first, second,third,....., and last row are respectively,
               23,21,19,....,5.
      Let the number of rows of rose plants be n.
      The sequence 23,21,19,...,5 is an A.P. with first term a = 23 , common difference d = -2 and nth term = 5.
                    an = a + ( n - 1 ) d
                     5 = 23 + ( n - 1 ) * -2
                     5 = 23 - 2n + 2
                    20 = 2n
                      n = 10.