Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs 400.

i)In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs 400.

ii)

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The fee charged every month by a school from Classes I to XII, when the monthly fee for Class I is Rs 250, and it increases by Rs 50 for the next higher class.

iii)

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The amount of money in the account of Varun at the end of every year when Rs 1000 is deposited at simple interest of 10% per annum.

iv)

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The number of bacteria in a certain food item after each second, when they double in every second.

Answers (1)

i)

Answer.          [Yes]

Solution.        

According to the question:

It is clear that the monthly fee charged from students is = 400 Rs.

Hence series is ; 400, 400, 400, 400 ……

the difference of the successive terms is same so It forms an AP with common difference d = 400 – 400 = 0

ii)

Answer.          [Yes]

Solution.        

According to the question:

Fees started Rs. 250 and increased by 50 Rs. from I to XII is

\\$Here first term( a\textsubscript{1})=250 common difference (d)=50 \\ a\textsubscript{1}=250\\ a\textsubscript{2}=250+50\\ =300\\ a\textsubscript{3}=300+50\\ =350\\ a\textsubscript{4}=350+50\\ =400\\ So the A.P. 250, 300, 350, 400$ \ldots $ \\                       

It forms an AP with common difference 50.

iii)

Answer.          [Yes]

Solution.         We know that: Simple interest = (P × R × T)/100

\\${ Here P = 1000}Rs \\$ R=10$\%$ P.a\\ T=1 year \\ S.I= \frac{1000\times 10\times 1}{100} \\ = 100\\ $Here common difference (d)=100 Rs and first term(a\textsubscript{1}) = 1000 Rs\\$ a\textsubscript{1}=1000 Rs\\ a\textsubscript{2}=1000+100\\ =1100 Rs\\ a\textsubscript{3}=1000+200\\ =1200 Rs\\ a\textsubscript{4}=1000+300\\ =1300 Rs\\ $So the A.P: 1000, 1100, 1200, 1300 $ \ldots $ \\                       

This is definite form an AP with common difference of SI=100 Rs.

iv)

Answer.          [No]

Solution.        

Let the number of bacteria = x

According to the question:

They double in every second.

\\$ \therefore x, 2x, 2(2x), 2(2 \times 2x)$ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ $ \ldots $ \\ Here a\textsubscript{1 }= x , a\textsubscript{2 }=2x, a\textsubscript{3 }=4x, a\textsubscript{4}=8x\\ x, 2x, 4x, 8x$ \ldots $ ..$ \ldots $ ..\\ a\textsubscript{2} - a\textsubscript{1} = 2x - x = x\\ a\textsubscript{3}- a\textsubscript{2} = 4x - 2x = 2x\\                       

Since the difference between the successive terms is not same therefore it does not form an AP.

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question