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Which of the following is/are TRUE
(A) Equal numbers are always in A.P. , G.P. and H.P.
\( \mathrm{P} \)
(B) If \( a, b, c \) be in H.P., then \( a-\frac{b}{2}, \frac{b}{2}, c-\frac{b}{2} \) will be in \( A P \)
W
(C) If \( G_{1} \) and \( G_{2} \) are two geometric means and \( A \) is the arithmetic mean inserted between two positive numbers, then the value of \( \frac{\mathrm{G}_{1}^{2}}{\mathrm{G}_{2}}+\frac{\mathrm{G}_{2}^{2}}{\mathrm{G}_{1}} \) is \( 2 \mathrm{~A} \).
(D) Let general term of a G.P. (with positive terms) with common ratio \( r \) be \( T_{k+1} \) and general term of another G.P. (with positive terms) with common ratio \( r \) be \( \mathrm{T}^{\prime}{ }_{k+1} \), then the series whose general term \( \mathrm{T}^{\prime \prime}{ }_{k+1}=\mathrm{T}_{k+1}+\mathrm{T}^{\prime}{ }_{k+1} \) is also a G.P. with common ratio \( r \).
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