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Find the first term of a HP whpse secpmd...

Find the first term of a HP whpse secpmd ter, os `(5)/(4)` and the third term is `(1)/(2)`.

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Let a be the first term. Then, `a,(5)/(4),(1)/(2)` are in HP.
Then, `(a-(5)/(4))/((5)/(4)-(1)/(2))=(a)/((1)/(2)) " " [" from above note "]`
` implies (4a-5)/(5-2)=2a`
` implies 4a-5=6a " or " 2a=-5`
` therefore a=-(5)/(2)`
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
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  13. Suppose four distinct positive numbers a(1),a(2),a(3),a(4) are in G.P....

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  15. If the sum of first n terms of an A.P. is cn^(2) then the sum of squar...

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  16. The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

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