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If the first two terms of a H.P. are 2//...

If the first two terms of a H.P. are `2//5and12//23` respectively. Then, largest term is

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The correct Answer is:
Second therm is the largest
Let the H.P. be `1/a,1/(a+d),1/(a+2d),1/(a+3d),..`
Then `1/a=2/5 and 1/(a+d)=12/13`
`rArra=5/2and d=-17/12`
Now, nth term of the H.P. is
`1/(a+(n-1)d)=12/(47-17n)`
So, the nth term is largest when 47-17n has the least positive value. Clearly, 12/(47-17n) is least for n=2. Hence, 2nd term is the largest term.
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