Mathematics
In a flower bed there are 43 rose plants in the first row, 41 in the second, 39 in the third and so on. There are 11 rose plants in the last row. How many rows are there and how many rose plants are there in the bed?
AP
1 Like
Answer
Given,
The number of rose plants in each row forms an Arithmetic Progression (A.P.):
43, 41, 39,……., 11.
a = 43
l = 11
d = 43 - 41 = -2
We know that,
∴ an = a + (n - 1)d
⇒ 11 = 43 + (n - 1)(-2)
⇒ 11 - 43 = (n - 1)(-2)
⇒ -32 = (n - 1)(-2)
⇒ = (n - 1)
⇒ n - 1 = 16
⇒ n = 16 + 1
⇒ n = 17
We know that,
Sum of n terms of an A.P. is given by,
∴ Sn = (a + l)
Total number of rose plants:
⇒ S17 = (43 + 11)
= (43 + 11)
= 15 ×
= 17 × 27
= 459.
Hence, number of rows = 17, total number of rose plants in the bed is 459.
Answered By
3 Likes
Related Questions
The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 8000 sets in 6th year, and 11300 in 9th year. Find the production in:
(i) first year
(ii) 8th year
(iii) total production in 6 years.
200 logs are stacked so that there are 20 logs in the bottom row, 19 logs in the next row, 18 in the next, and so on. How many rows are formed and how many logs are there in the top row?
A man saved ₹ 33,000 in 10 months. In each month after the first, he saves ₹ 100 more than he did in the preceding month. How much did he save in the first month?
The general term of an A.P. whose first term is a and common difference is d, is given by:
Tn = 2a + (n − 1)d
Tn =
Tn = a + (n − 1)d
Tn =