Question

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

Answer 1

Answer:

100

Step-by-step explanation:

As the com. dif. is same, let that be 'd'.

For first AP:

Let first term is a, 100th term is

= > a + (100 - 1)d

= > a + 99d

For 2nd AP:

Let first term be 'x', 100th term is

= > x + (100 - 1)d

= > x + 99d

Difference in their 100th term is:

= > (a + 99d) - (x + 99d) = 100

= > a + 99d - x - 99d = 100

= > a - x = 100

Difference in 1000th terms is:

= > {a + (1000 - 1)d} - {x + (1000 - 1)d}

= > a + 999d - x - 999d

= > a - x

= > 100 { from above, a - x = 100}

Answer 2

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