NCERT/CBSE MATHS Class 10 Ex-5.2 Q No.12 Solutions : Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?
Hy Friends Welcome On NCERT MATHS SOLUTIONS !! Today we are going to solve the Question : ”Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?” of Exercise 5.2 Question No 12 Solutions (Arithmetic Progressions) of Class 10th, which will prove to be very helpful for you.
CBSE/NCERT MATHS Class 10 Ex-5.2 Q No. 12 Solutions
If you are a student of CBSE, today we are going to give you the CBSE / NCERT Chapter : Arithmetic Progressions Exercise 5.2 Question No – 12 Solutions . Hope you like this post about Class 10th Maths Solution.
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Arithmetic Progressions CHAPTER : 5
n this progression, for a given series, the terms used are the first term, the common difference between the two terms and nth term.
Suppose, a1, a2, a3, ……………., an is an AP, then; the common difference “ d ” can be obtained as; In this progression, for a given series, the terms used are the first term, the common difference between the two terms and nth term.
a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d
Exercise- 5.2 Question No. 12 :
Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?
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 … (i)
Difference between 1000th terms of these A.P.s
(a1 + 999d) − (a2 + 999d) = a1 − a2
From equation (i),
This difference, a1 − a2 = 100
Hence, the difference between 1000th terms of these A.P. will be 100.
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