NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 12

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 12

Question:

Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?.

Given:

Let the two arithmetic progressions be {an} and {bn}. 

They have the same common difference, say 'd'.

a100 - b100 = 100

To Find:

The difference between their 1000th terms, i.e., a1000 - b1000.

S

Formula:

The nth term of an AP is given by an = a1 + (n-1)d, where 

a1 is the first term and d is the common difference.

Solution:

a100 = a1 + 99d

b100 = b1 + 99d

a100 - b100 = (a1 + 99d) - (b1 + 99d) = a1 - b1 = 100

a1000 = a1 + 999d

b1000 = b1 + 999d

a1000 - b1000 = (a1 + 999d) - (b1 + 999d) = a1 - b1

Since a1 - b1 = 100, 

a1000 - b1000 = 100

Result:

The difference between their 1000th terms is 100.

© Kaliyuga Ekalavya. All rights reserved.

Comments

Post a Comment