Q17.Ankita deposited Rs. 200into her daughter’s piggy bank when she turned one-year-old.since then she has deposited the same amount of money increasedby Rs 50every year into her piggy bank.The amount of money in her piggy bank beginning from her first year were (inrupees)were 200, 250, 300.........respectively. a)The amount for the next 5thand 6thbirthday of the given A.P. isi)400,500 ii) 450, 550 iii) 400, 450 iv) 450,500b)Find the commondifference of given A.P. is i)20 ii) 50iii) 100 iv) 150c)Find the total money collected on her 10thbirthday in the piggy banki)2550 ii) 4250 iii) 3250 iv) 6250d)Amount deposited in the piggy bank on her 21stbirthday is i)1400 ii) 1200 iii) 1600 iv) 1800e)In which year she will deposit 1000 rupees in piggy banki)17thii) 18thiii) 19thiv) none of these
Answers
Given:
The AP formed of the money deposited = 200, 250, 300, 350.....
To find:
- The amount of money in the piggy bank for the 5th and 6th birthday.
- The common difference of the AP.
- The total money collected on her 10th birthday in the piggy bank.
- In which year she will deposit 1000 rupees in piggy bank.
Solution:
Amount of money for the 5th and 6th birthday:
a₅ = a + (n-1)d
Where a₅= amount deposited on 5th birthday
a = initial amount deposited
n = 5
d = difference of AP
Putting the values we get:
a₅ = 200 + (5-1)*50
a₅ = 200 + 4*50
a₅ = 200+ 200
a₅ = Rs. 400
Similarly amount deposited for 6th birthday:
a₆ = a + (n-1)d
a₆ = 200 + (6-1)*50
a₆ = 200 + 5*50
a₆ = 200 + 250
a₆ = Rs. 450
The correct option is (iii).
The common difference of AP = difference between 2 terms = 250-50 =50
The correct option is (ii).
Total money collected on 10th birthday= Sum of 10 terms of the given AP
S = n/2[2a + (n-1)d]
S = 10/2[ 2*200 + (10-1)50]
S = 5[400 + 450]
S = 5*850 = 4250
The correct option is (ii).
Amount deposited on 21st birthday:
a₂₁ = a + (n-1)d
= 200 + (21-1)50
= 200 + 1000
= 1200
The correct option is (ii).
In which year will she deposit Rs. 1000.
We know that aₙ = a + (n-1)d
1000 = 200 + (n-1)50
800 = (n-1)50
16 = (n-1)
n = 17
The correct option is (i).
Answer:
amount the amount in rupees for the next fifth and sixth birthday of the given AP is