Question

390 plants are to be planted in a garden in a number of row. There are 40 plants in the 1st row, 38 plants in 2nd row, 36 plants in 3rd row and so on. In how many rows the 390 plants are planted? Find the number of plants in last row also.

Answer 1

Answer:

Step-by-step explanation:

Firstly total no of plant in 3 rows = 40+38+36= 122

so to plant 390 we need:

so in 4 row plant will be 34

in 5 row = 32

in 6 row = 30

in  7 row = 28

in last row we will have 28 flowers

Answer 2

In 15 rows 390 plants are planted.

12 plants are planted in the last row.

Step-by-step explanation:

A.P = a1, a2, a3, _ _ _ _ an

A.P = 40, 38, 36, _ _ _ _ an

d = 38 - 40 = -2

a = 40

Sum of A.P = 390

Let the no. of rows in which 390 plants are planted be n,

n/2[2a + (n - 1)d] = 390

n/2[2 x 40 + (n - 1)(-2)] = 390

n/2[80 + (n - 1)(-2)] = 390

n[80 -2n + 2] = 390 x 2

n[80 - 2n + 2] = 780

80n - 2n² + 2n = 780

-2n² + 82n - 780 = 0

n² - 41n + 390 = 0

n² - 26n - 15n + 390 = 0

n(n - 26) - 15(n - 26) = 0

(n - 26)(n - 15) = 0

n = 26, 15

If n = 26 then Sn = 728

and if n = 15 then n = 390

So, n = 15

Let the no. of plants in the last row be ,

= a + (n - 1)d

= 40 + (15 - 1)(-2)

= 40 + 14(-2)

= 40 - 28

= 12

I hope this answer is helpful for you