Two AP have the same common difference. The difference between their 100th terms is 111222333. The d

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23 Mar 2013 AP

Two AP have the same common difference. The difference between their 100th terms is 111222333. The difference between their 10000th term will be...

OPtion

1) 111122223333
2) 112233
3) 111222333
4) 222111333
5) 333222111
6) 123123123
7) 321321321
8) 231231231
9) 0
10) None of these

Solution

let first AP first terms be x and difference d
and let second AP first terms be y and difference d (given common difference same)
By the given condition
first AP (Ist)t100 = x + 99d (i)
second AP (IInd)t100 = y + 99d (ii)
solve (i) and (ii)
therefore x-y = 111222333 (iii)
then
(Ist) t10000 = x + 9999d (iv)
(IInd)t10000 = y + 9999d (v)
(Ist)t10000 + (IInd)t10000 = x - y
= 111222333 (By (iii) equation
same (option 3)

Correct Option: 3 Best Solution (1)

Vinay Sipani    11 years AGO

Tn1 - Tn2 = (a1 - a2) + (n-1)(d1 - d2)
but d1 = d2
=> Tn1 - Tn2 = a1 - a2 = 111222333

i.e. difference of nth terms of both APs remains the same.
=> Difference of 10000th terms = 111222333

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