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Answer 1

Question :

Due to corona pandemic Anjali lost her job and was left with only 40,000 rupees in her bank account. To carry out her monthly expenses she withdraws rupees 5000 in the first month and realized that she had to withdraw rupees 200 more every month additional to the previous month's withdrawal.

(i) Which of the following is the correct arithmetic progression?

a) 5000, 5100 , 5300, ...

b) 5000, 5200, 5400, ...

 c) 5000, 4800, 4600, ...

 d) None of the above

Answer :

In the first month, she withdraws Rs. 5000

In the second month, she withdraws Rs 200 more than the previous month's withdrawal.

 So, 5000 + 200 = 5200

In the third month, she withdraws Rs 200 more than the second month's withdrawal.

 So, 5200 + 200 = 5400

Therefore, correct option is (b) 5000 , 5200 , 5400 , ...

(ii) Total amount withdrawn by Anjali at the end of 6th month.

a) 30000

b) 32000

c) 33000

d) 34000

Answer :

Method - 1 :

 In the first month, she withdraws Rs. 5000

 In the second month, she withdraws Rs 5200

 In the third month, she withdraws Rs 5400

 In the fourth month, she withdraws Rs 5400 + 200 = Rs 5600

 In the fifth month, she withdraws Rs 5600 + 200 = Rs 5800

 In the sixth month, she withdraws Rs 5800 + 200 = Rs 6000

To get the total amount withdrawn by her at the end of 6th month, add them.

Rs. 5000 + 5200 + 5400 + 5600 + 5800 + 6000

Rs. 33000

Method - 2 : [By using formula]

The arithmetic sequence is 5000 , 5200 , 5400 , ...

• first term, a = 5000

• common difference, d = 5200 - 5000 = 200

Now, to find the total amount withdrawn at the end of 6th month, we have to find the sum of the amount withdrawn for 6 months.

 $\boxed{\tt S_n=\dfrac{n}{2}[2a+(n-1)d]}$

 S₆ = 6/2 [2(5000) + (6 - 1)(200)]

 S₆ = 3 [10000 + 5(200)]

 S₆ = 3 [10000 + 1000]

 S₆ = 3[11000]

 S₆ = 33000

Hence, correct option is (c)

(iii) How much amount is left in her bank account by the end of 6th month?

a) 7000

 b) 5000

 c) 9000

 d) 3000

Answer :

Amount in her bank account initially = Rs 40000

Total amount withdrawn at the end of 6th month = Rs 33000

The amount left in her bank account = Rs. 40000 - Rs. 33000 = Rs 7000

Hence, correct option is (a)

(iv) What is the common difference for the correct Arithmetic Progression?

Answer :

The correct Arithmetic Progression is 5000 , 5200 , 5400 ,.... [ question (i) ]

We know, common difference is the difference between a term and it's preceding term.

So, d = 5200 - 5000 = 200

Hence, common difference = 200

Answer 2

Answ

900

300

600

i am good