Happy Diwali!

Algebra Level 5

Suppose that s n s_{n} represent s 1 , s 2 , s 3 , . . . . . . s_{1},s_{2},s_{3},...... an strictly increasing sequence of positive integers such that the sub sequences

s s 1 , s s 2 , s s 3 , . . . . . . . . a n d s s 1 + 1 , s s 2 + 1 , s s 3 + 1 , . . . . . . \Large{s_{s_{1}}, s_{s_{2}}, s_{s_{3}}, ........ \qquad and \qquad s_{s_{1}+1}, s_{s_{2}+1}, s_{s_{3}+1},......}

are in Arithmetic Progression, Then s n s_{n} are in:-

Happy And Prosperous Diwali to all

None of these Harmonic Progression Arithmetic Progression Geometric Progression

Department 8 by Department 8 , 27, Israel

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