Two arithmetic progressions have first terms and common differences respectively.

MATHEMATICS · Multi-part · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

Two arithmetic progressions have first terms

a_1,\,a_2

and common differences

d_1,\,d_2

respectively. (i) Write the general expression for the

n

-th term of each progression using the given symbols. (ii) If the

n

-th terms of the two progressions are equal, obtain the relation connecting

n,\,a_1,\,a_2,\,d_1

and

d_2

. (iii) Explain the condition on

d_1

and

d_2

under which such an

n

can exist as a positive integer.