1.

The numbers `3^(2sin2alpha-1),14and3^(4-2sin2alpha)` form first three terms of A.P., its fifth term isA. `-25`B. `-12`C. 40D. 53

Answer» Correct Answer - D
Since,`3^(2sin2alpha-1),14and3^(4-2sin2alpha)`
`:." "2xx143^(2sin2alpha-1)+3^(4-2sin2alpha)`
`rArr" "28=(a)/(3)+(3^(4))/(a)`, where `a=3^(2sin2alpha)`
`rArr" "a^(2)-84a+243=0`
`rArr" "(a-81)(a-3)=0`
`rArr" "a=81,a=3`
`rArr" "3^(2sin2alpha)=3^(4)or,3^(2sin2alpha)=3`
`rArr" "2sin2alpha=1" "[because2sin2alpha!=4]`
`rArr" "sin2alpha=(1)/(2)rArr2alpha=(pi)/(6)`
Thus, the first three terms of the A.P. are 1,14,27.
Hence, its fifth term is 53.


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