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 thereare 5 rose plants in the last row how many rows are there in the flower bed​

Answer 1

Given that, 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.

So, from the above information, we have A.P. = 23, 21, 19,..................., 5

We have to find the number of rows in the flower bed.

Let us assume that there are 'n' number of rows in the flower bed.

A.P. 23, 21, 19,.................., 5

So,

First-term (a) = 23

Common difference (d) = a2 - a1 = 21 - 23 = -2

Last term (an) = 5

We know that,

an = a + (n - 1)d

Substitute the known values form above

→ 5 = 23 + (n - 1)(-2)

→ 5 - 23 = (n - 1)(-2)

→ - 18 = (n - 1)(-2)

→ (-18)/(-2) = n - 1

→ 9 = n - 1

→ 9 + 1 = n

→ 10 = n

Therefore,

There are 10 rows in the flower bed.

Answer 2

Answer:

In First Row we Have 23 rose plants, In Second 21, 19 in Third and so, and In Last Row there is 5 rose plants. This is in Arithmetic Progresion.

• First Term ( a ) = 23
• Common Difference ( d ) = 21 – 23 = 19 – 19 = – 2
• Last Term ( Tn ) = 5
• Number of Terms ( n ) = ?

☯ Tn Term of the AP :

↠ Tn = a + (n – 1)d

• putting the values

↠ 5 = 23 + (n – 1)(– 2)

↠ 5 = 23 – 2n + 2

↠ 5 = 25 – 2n

↠ 2n = 25 – 5

↠ 2n = 20

• Dividing both term by 2

↠ n = 10

∴ There are 10 rows of Rose Flower Bed.