Question

# The sum of first four terms of a geometric progression (G.P.) is 6512 and the sum of their respective reciprocals is 6518. If the product of first three terms of the G.P. is 1, and the third term is α, then 2α is

Solution

## Let the first four terms be a,ar,ar2,ar3. a+ar+ar2+ar3=6512     ⋯(1)  and 1a+1ar+1ar2+1ar3=6518 ⇒1a(r3+r2+r+1r3)=6518     ⋯(2)  (1)(2), we get a2r3=1812=32 Also, a3r3=1 ⇒a(32)=1⇒a=23 49r3=32 ⇒r3=3323⇒r=23 α=ar2=23.(32)2=32 ∴2α=3

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