Question

# A geometric progression consists of an even number of terms. The sum of all the terms is three times that of the odd terms, the common ratio of the progression will be-

Solution

Let the sequence be ( a, a r^{2}, a r^{3}, a r^{4}, ldots ldots ldots )

Sum of terms in odd positions ( =frac{aleft(r^{2 n}-1right)}{r^{2}-1}=m ) (say)

Sum of terms in even position ( =frac{a rleft(r^{2 n}-1right)}{r^{2}-1}=n ) (say)

Sum of all the terms in sequence =

( m+n=3 m )

( Longrightarrow n=2 m )

( frac{a rleft(r^{2 n}-1right)}{r^{2}-1}=2 times frac{aleft(r^{2 n}-1right)}{r^{2}-1} )

( r=2 )