Question

plzz answer it step by step​

Answer 1

☆GIVEN:

There are 25 rose plants in the first row, 23 in the second , 21 in the third and 3 in the last row.

☆TO FIND:

1. No of rows in the flower beds?

2. Total number of rose plants in the flower bed?

☆CONCEPT USED :

We use the concept and formula of AP here as there is a sequence of rose plants in each row in a flower bed.

$nth \: term = a + (n - 1)d$

where;

a = first term

d = common difference

☆SOLUTION:

series = 25 , 23, 21, ................3

Now,

a = 25

d = 23 - 25

d = -2

Answer 1:

n = ?

$t(n) = 25 + (n - 1) - 2 \\ 3 = 25 - 2n + 2 \\ 3 = 27 - 2n \\ 3 - 27 = - 2n \\ - 24 = - 2n \\ n = 12$

$</u></strong><strong><u>\</u></strong><strong><u>h</u></strong><strong><u>u</u></strong><strong><u>g</u></strong><strong><u>e</u></strong><strong><u>\</u></strong><strong><u>b</u></strong><strong><u>l</u></strong><strong><u>u</u></strong><strong><u>e</u></strong><strong><u> </u></strong><strong><u>{</u></strong><strong><u>no \: of \: rows \: = 12</u></strong><strong><u>}</u></strong><strong><u>$

ANSWER 2 :

For second case we have to find total number of flower we use the sum formula;

$s(n) = \frac{n}{2} (a + l) \\ (l = last \: term)$

$s(12) = \frac{12}{2} (25 + 3) \\ s(12) = 6 \times 28 \\ s(12) = 168$

$</u></strong><strong><u>\</u></strong><strong><u>h</u></strong><strong><u>u</u></strong><strong><u>g</u></strong><strong><u>e</u></strong><strong><u>\</u></strong><strong><u>p</u></strong><strong><u>u</u></strong><strong><u>r</u></strong><strong><u>p</u></strong><strong><u>l</u></strong><strong><u>e</u></strong><strong><u> </u></strong><strong><u>{</u></strong><strong><u>total \: rose \: plants \: = 168</u></strong><strong><u>}</u></strong><strong><u>$

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