# 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
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#### APPEARS IN

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