Test Index

Sequence and Series

Question : 46 of 86

Marks: +1, -0

Solution:

Concept:

For two arithmetic progressions with the same common difference, the difference between any corresponding terms is constant.

Explanation:

Let the first terms be

a_1

and

a_2

, and the common difference be

d

The

100^{\text{th}}

terms are

a_1 + 99d

and

a_2 + 99d

Their difference is

(a_1 + 99d) - (a_2 + 99d) = a_1 - a_2

, given as

111222333

The

1,000,000^{\text{th}}

terms are

a_1 + 999999d

and

a_2 + 999999d

Their difference is also

a_1 - a_2 = 111222333

Thus, the difference is the same for all terms.

Answer:

111222333

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