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Question

Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?


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Solution

  • Step 1: Finding out the difference between their 1000th terms.

Let, the first term of two APSs be a1 and a2 respectively

And the common difference between these APS be d.

For the first A.P.,we know,

an=a+(n-1)d

Therefore,

a100=a1+(100-1)d=a1+99da1000=a1+(1000-1)d=a1+(999d)

  • Step 2: Finding out the difference between their 1000th terms.

For second A.P., we know,

an=a+(n-1)d

Therefore,

a100=a2+(100-1)da2+99da1000=a2+(1000-1)da2+999d

Given that, difference between 100th term of the two APs=100

Therefore, (a1+99d)-(a2+99d)=100a1-a2=100(1)

Difference between 1000th terms of the two APs

a1+999d-(a2+999d)=a1-a2Fromequation(1)

This difference, a1-a2=100

Hence, the difference between 1000th terms of the two A.P. will be 100.


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