Question

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 in the flower bed ?​

Answer 1

✬ Rows = 17 ✬

Step-by-step explanation:

Given:

• 43 rose plants are in first row.
• 41 rose plants in second & 39 in the third row.
• In last row there are 11 rose plants.

To Find:

• How many rows are there in the flower bed ?

Solution: Let the number of rows in flower bed be n.

Arranging all the number of rose plants in a series we got

• 43 , 41 , 39...................11

Let's check whether this series forms a AP or not.

• a = 43
• a² = 41
• a³ = 39
• l = 11

Finding common difference between these terms

➮ d = a² – a = 41 – 43 = –2

➮ d = a³ – a² = 39 – 41 = –2

Hence, d is same so given series are in AP

So now we have

• a {first term} = 43
• d = –2
• Last term = 11

As we know that nth term of AP series is given by

★ aⁿ = a + (n – 1)d ★

$\implies{\rm }$ 11 = 43 + (n – 1)–2

$\implies{\rm }$ 11 = 43 + (–2n + 2)

$\implies{\rm }$ 11 = 43 – 2n + 2

$\implies{\rm }$ 11 = 45 – 2n

$\implies{\rm }$ 11 – 45/–2 = n

$\implies{\rm }$ –34/–2 = 17 = n

Hence, there are 17 rows in the flower bed.

Answer 2

♧Answer♧

ʟᴇᴛ ᴛʜᴇ ɴᴏ. ᴏꜰ ʀᴏꜱᴇꜱ ɪɴ ꜰʟᴏᴡᴇʀ ʙᴇᴅ ʙᴇ x.

ʙʏ ᴀʀʀᴀɴɢɪɴɢ ᴛʜᴇ ꜱᴇʀɪᴇꜱ, ᴡᴇ ɢᴇᴛ: 43,41,39.......11

ʜᴇʀᴇ,

ᴀ = 43

ᴀ2 = 41

ᴀ3 = 39

ʟᴀꜱᴛ ᴛᴇʀᴍ = 11

ᴄᴏᴍᴍᴏɴ ᴅɪꜰꜰᴇʀᴇɴᴄᴇꜱ,

ᴅ = 41 - 44 = -2

ɴᴏᴡ,

ɴ = ᴀ+(ɴ-1)ᴅ

11 = 43 +(ɴ-1) (-2)

11 = 43 - 2ɴ + 2

11 = 45 - 2ɴ

ɴ = 17

ʜᴇɴᴄᴇ, ᴛʜᴇʀᴇ ᴀʀᴇ 17 ʀᴏᴡꜱ ɪɴ ꜰʟᴏᴡᴇʀ ʙᴇᴅ.