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Question

Two AP's have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

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Solution

an=a+(n1)d

100th term will be,

a100=a+(1001)d

a100=a+99d

100th term of 1st Ap = a + 99d

2nd AP will be,

bn=bn+(n1)d

b100=b+99d

a100b100=100

(a+99d)(b+99d)=100

ab=100...(1)

Difference between 1000th term,

=a1000b1000

=a+(10001)d)[b+(10001)d]

=ab+999d999d

=100



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