Two Arithmetic Progressions Have the Same Common Difference. the Difference Between Their 100th Terms is 100, What is the Difference Between Their L000th Terms? - Mathematics

Question

Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their l000th terms?

Solution

Here, we are given two A.P sequences which have the same common difference. Let us take the first term of one A.P. as a and of other A.P. as a’

Also, it is given that the difference between their 100th terms is 100.

We need to find the difference between their 100th terms

So, let us first find the 100th terms for both of them.

Now, as we know,

a_n = a + (n - 1)d

So for 100 th term of first A.P (n = 100)

a_100 = a + (100 - 1)d

= a + 99d

Nw for 100 th term of second A.P (n = 100)

a_100 = a + (100 - 1)d

= a + 99d

Now, for 100 th term of second A.P (n = 100)

a'_100 = a' + (100 - 1)d

= a' + 99d

Now we are given

a_100 - a'_100 = 100

On substituting the values we get

a + 99d - a' - 99d = 100

a - a' = 100 .....(1)

Now we need the difference between the 1000 th term of both the A.P.

So for 1000 th term of second A.P. (n = 1000)

a'_1000 = a' + (1000 - 1)d

= a' + 999d

So,

a_1000 - a'_1000 = (a + 999d) - (a' + 999d)

=a + 999d - a' - 999d

= a- a'

= 100        (Using 1)

Therefore the difference ebetween the 1000 th terms of both the arithmetic progression will be  100

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RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 5: Arithmetic Progression
Exercise 5.4 | 27 | Page no. 25
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 5: Arithmetic Progression
Exercise 5.4 | 27 | Page no. 25

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Two Arithmetic Progressions Have the Same Common Difference. the Difference Between Their 100th Terms is 100, What is the Difference Between Their L000th Terms? Concept: Arithmetic Progression.