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Show that the progression 1/2, (-1)/3, 2...

Show that the progression `1/2, (-1)/3, 2/9, (-4)/27`, ... is a GP. Write down its first term and find the common ratio.

Text Solution

Verified by Experts

We have
`((-1)/3) div 1/2 =((-1)/3xx2)=(-2)/3, 2/9 div ((-1)/3)={2/9xx3/((-1))}=(-2)/3, ((-4)/27) div 2/9=((-4)/27xx9/2)=(-2)/3`.
So, the given progression is a GP in which `a=1/2` and `r=(-2)/3`
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