Question

Ramesh wants to participate in 200 m race. He currently can run that distance in 45 sec.

But he wants to do that in 30 sec. With each day practice, it takes 2 sec less.

(a) Which of the following forms an AP for the above situation?

(i) 45,90 ,180….. (ii) 45, 47, 49….. (iii) 45, 43, 41…. (iv) None of these

(b) What is the minimum number of days he need to practice till his goal is accomplished

(i) 8 days (ii) 8.5 days (iii) 9 days (iv) None of these

(c) Which of the following terms is not in the AP of the given situation.

(i) 31 (ii) 30 (iii) 29 (iv) 27

(d) The nth term of the sequence a, a+d, a+2d…….

(i) a+nd (ii) a-(n-1)d (iii) a+(n-1)d (iv) n+ nd

(e) By practicing how many seconds he will take on 6th day

(i) 39 sec (ii) 37 sec (iii) 35 sec (iv)None of these​

Answer 1

Answer:

a=45,43,41....

b=8.5days

c=30

d=a+(n-1)×d

e=35 sec

Answer 2

Step-by-step explanation:

Given that:

Ramesh wants to participate in 200 m race. He currently can run that distance in 45 sec.

But he wants to do that in 30 sec. With each day practice, it takes 2 sec less.

To find:

(a) Which of the following forms an AP for the above situation?

(i) 45,90 ,180….. (ii) 45, 47, 49….. (iii) 45, 43, 41…. (iv) None of these

(b) What is the minimum number of days he need to practice till his goal is accomplished

(i) 8 days (ii) 8.5 days (iii) 9 days (iv) None of these

(c) Which of the following terms is not in the AP of the given situation.

(i) 31 (ii) 30 (iii) 29 (iv) 27

(d) The nth term of the sequence a, a+d, a+2d…….

(i) a+nd (ii) a-(n-1)d (iii) a+(n-1)d (iv) n+ nd

(e) By practicing how many seconds he will take on 6th day

(i) 39 sec (ii) 37 sec (iii) 35 sec (iv)None of these

Solution:

(a) Which of the following forms an AP for the above situation?

(i) 45,90 ,180….. (ii) 45, 47, 49….. (iii) 45, 43, 41…. (iv) None of these

Ans: Started from 45 sec Ramesh reduces his time 2 sec everyday,Thus

a= 45

d= -2

Hence AP= 45,43,41...

Option (iii) is correct

(b) What is the minimum number of days he need to practice till his goal is accomplished

(i) 8 days (ii) 8.5 days (iii) 9 days (iv) None of these

Ans:

His aim is to reduce his race time to 30 sec

an= 30 sec

a= 45

d= -2

n=?

$a</strong><strong>_</strong><strong>n = a + (n - 1)d \\ \\ 30 = 45 + (n - 1)( - 2) \\ \\ 30 - 45 = - 2(n - 1) \\ - 15 = - 2(n - 1) \\ \\ n - 1 = \frac{15}{2} \\ \\ n - 1 = 7.5 \\ \\ n = 8.5$

n= 8.5 days

Option (ii) is correct.

(c) Which of the following terms is not in the AP of the given situation.

(i) 31 (ii) 30 (iii) 29 (iv) 27

Ans:

45,43,41,39,37,35,33,31,29,27...

30 is not the term of AP.

Option (ii) is correct.

(d) The nth term of the sequence a, a+d, a+2d…….

(i) a+nd (ii) a-(n-1)d (iii) a+(n-1)d (iv) n+ nd

Ans: nth term of sequence is

$a_n = a + (n - 1)d$

Option (iii) is correct.

(e) By practicing how many seconds he will take on 6th day

(i) 39 sec (ii) 37 sec (iii) 35 sec (iv)None of these

Ans:

Find 6th term of AP

$a_6 = a + 5d \\ \\ a_6 = 45 - 10 \\ \\ a_6 = 35$

35 seconds

Option (iii) is correct.

Hope it helps you.

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