Mathematics

Problem

An arithmetic progression (AP) and a geometric progression (GP) both have the same positive first term

a

. The AP has common difference

d>0

while the GP has common ratio

0<r<1

. For every integer

n\ge 2

, which one of the following statements is always true? a)

S_{AP}=S_{GP}

S_{AP}<S_{GP}

S_{AP}>S_{GP}

d) No definite comparison can be made between

S_{AP}

and

S_{GP}