two APs have the same comman difference The difference between their 100th terms is 100 what is the difference between their 1000th terms?
Answers 1
Let the AP's be an and
let first term of an be a1
and first term of bn be b1
the common difference given is same lets suppose that is d
and we know nth term of an AP be:
an= a+(n-1)
So, 100th term of an be
a100 = a1+( 00-1)
a100= a1+99d
and, the 100th term of bn
b100 = b1+(00-1)
b100 = b1+99d
Given that difference of a100 and b100 is 100 ;
a100-b100 = 100
[a1+99d] - [ b1 +99d] = 100
a1-b1 =. 100
Now, difference between their 1000th terms be;
=[a1+999d] - [ b1+999d ]
= a1 - b1
=100
Hence, the answer is 100
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