Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000thterms? - Mathematics

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

Solution

Let the first term of these A.P.s be a1 and a2 respectively and the common difference of these A.P.s be d.

For first A.P.,

a100 = a1 + (100 − 1) d

= a1 + 99d

a1000 = a1 + (1000 − 1) d

a1000 = a1 + 999d

For second A.P.,

a100 = a2 + (100 − 1) d

= a2 + 99d

a1000 = a2 + (1000 − 1) d

= a2 + 999d

Given that, difference between

100th term of these A.P.s = 100

Therefore, (a1 + 99d) − (a2 + 99d) = 100

a1 − a2 = 100 (1)

Difference between 1000th terms of these A.P.s

(a1 + 999d) − (a2 + 999d) = a1 − a2

From equation (1),

This difference, a1 − a= 100

Hence, the difference between 1000th terms of these A.P. will be 100.

Concept: nth Term of an AP
Is there an error in this question or solution?
Chapter 5: Arithmetic Progressions - Exercise 5.2 [Page 106]

APPEARS IN

NCERT Class 10 Maths
Chapter 5 Arithmetic Progressions
Exercise 5.2 | Q 12 | Page 106
Share