Is the sequence formed in the following situations an A.P. (i) Number of students left in the school auditorium from the total strength of 1000 students when they leave the auditorium in batches of 25.(ii) The amount of money in the account every year when Rs. 100 are deposited annually to accumulate at compound interest at 4% per annum.
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i) Given:
Total strength of students in the auditorium= 1000
Number of students left in the Auditorium when first batch of 25 students leaves the auditorium= 1000 - 25 = 975
Number of students left in the Auditorium when second batch of 25 students leaves the auditorium= 975 - 25 = 950
Number of students left in the Auditorium when third batch of 25 students leaves the auditorium= 950 - 25 = 925 and so on…
Thus, the number of students lap in auditorium at different stages are:
1000, 975, 950, 925,.......
Clearly it is an A.P with first term(a)= 1000 common difference(d) = -25.
ii) If P is the principal and R% per annum is the rate of interest compounded annually then, the amount (A) at the end of n years.
A = P (1 + R/100)ⁿ
Given: P = ₹ 100, R= 4
A= 100(1+4/100)ⁿ
A= 100 (1 + 1/25)ⁿ
A = 100 (26/25)ⁿ
A= 100 × (1.04)ⁿ
The amount of money in the account at the end of different years is given by:
₹ 100 × (1.04)ⁿ , 100 × (1.04)² , 100 × (1.04)³,.....
Or ₹ 104 , ₹ 108.16 , ₹ 112.48,.....
Clearly it is not forming an A.P.
HOPE THIS WILL HELP YOU....
Total strength of students in the auditorium= 1000
Number of students left in the Auditorium when first batch of 25 students leaves the auditorium= 1000 - 25 = 975
Number of students left in the Auditorium when second batch of 25 students leaves the auditorium= 975 - 25 = 950
Number of students left in the Auditorium when third batch of 25 students leaves the auditorium= 950 - 25 = 925 and so on…
Thus, the number of students lap in auditorium at different stages are:
1000, 975, 950, 925,.......
Clearly it is an A.P with first term(a)= 1000 common difference(d) = -25.
ii) If P is the principal and R% per annum is the rate of interest compounded annually then, the amount (A) at the end of n years.
A = P (1 + R/100)ⁿ
Given: P = ₹ 100, R= 4
A= 100(1+4/100)ⁿ
A= 100 (1 + 1/25)ⁿ
A = 100 (26/25)ⁿ
A= 100 × (1.04)ⁿ
The amount of money in the account at the end of different years is given by:
₹ 100 × (1.04)ⁿ , 100 × (1.04)² , 100 × (1.04)³,.....
Or ₹ 104 , ₹ 108.16 , ₹ 112.48,.....
Clearly it is not forming an A.P.
HOPE THIS WILL HELP YOU....
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