If a, ;b, ;c are in A.P. and a, ;b, ;d in G.P., then a, ;a - b, ;… - Vidyadip

MCQ

If $a,\;b,\;c$ are in $A.P.$ and $a,\;b,\;d$ in $G.P.$, then $a,\;a - b,\;d - c$ will be in

A
$A.P.$
✓
$G.P.$
C
$H.P.$
D
None of these

✓

Answer

Correct option: B.

$G.P.$

b
(b) Given that $a,\;b,\;c$ are in $A.P.$

$ \Rightarrow b = \frac{{a + c}}{2}$…..$(i)$

and ${b^2} = ad$….. $(ii)$

Hence $a,\;a - b,\;d - c$ are in $G.P. $ because

${(a - b)^2} = {a^2} - 2ab + {b^2} = a(a - 2b) + ad$

$ = a(a - a - c) + ad = ad - ac$.

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