1. In which of the following situations, does the list of numbers involved make an arichmedic
@ The taxi fare after each km when the fare is? 15 for the first km and #8 for each
progression, and why?
additional km.
4
in The amount of air present in a cylinder when a vacuum pump removes of the
air remaining in the cylinder at a time.
m The cost of digging a well after every metre of digging, when it costs * 150 for the
first metre and rises by 50 for each subsequent metre.
(iv) The amount of money in the account every year, when * 10000 is deposited at
compound interest at 8 % per annum.
Answers
Answer:
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Step-by-step explanation:
11th
Maths
Sequences and Series
Arithmetic Progression
In which of the following s...
MATHS
In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?
(i) The taxi fare after each km when the fare is Rs.15 for the first km and Rs. 8 for each additional km.
(ii) The amount of air present in a cylinder when a vacuum pump removes
4
1
of the air remaining in the cylinder at a time.
(iii) The cost of digging a well after every metre of digging, when it costs Rs. 150 for the first metre and rises by Rs. 50 for each subsequent metre.
(iv) The amount of money in the account every year, when Rs. 10000 is deposited at compound interest at 8 % per annum.
MEDIUM
VIDEO EXPLANATION
ANSWER
(i) Fare for first km = Rs. 15
Fare for second km = Rs. 15+8= Rs 23
Fare for third km = Rs. 23+8=31
Here, each subsequent term is obtained by adding a fixed number (8) to the previous term.
Hence, it is in A.P.
(ii) Let us assume, initial quantity of air =1 .....1)
Therefore, quantity removed in first step =
4
1
Remaining quantity after first step
1−
4
1
=
4
3
....2)
Quantity removed in second step
=
4
3
×
4
1
=
16
3
Remaining quantity after second step
=
4
3
−
16
3
=
16
9
....3)
Here, each subsequent term is not obtained by adding a fixed number to the previous term.
Hence, it is not an AP.
(iii) Cost of digging of 1
st
meter =150
Cost of digging of 2
nd
meter =150+50=200
Cost of digging of 3
rd
meter =200+50=250
Here, each subsequent term is obtained by adding a fixed number (50) to the previous term.
Hence, it is an AP.
(iv) Amount in the beginning = Rs. 10000
Interest at the end of 1
st
year @ 8% = 10000×8%=800
Thus, amount at the end of 1
st
year =10000+800=10800
Interest at the end of 2
nd
year @ 8% = 10800×8%=864
Thus, amount at the end of 2
nd
year =10800+864=11664
Since, each subsequent term is not obtained by adding a fixed number to the previous term; hence, it is not an AP.