$\begin{array}{1 1} -2,1,4,16 \\ -3,1,5,25 \\ -1,2,5,25 \\ 1,2,3,9 \end{array}$

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Answer : (a) -2,1,4,16

Explanation : Let the 4 numbers be a,b,c,d

$a,b,c\;in\;AP\quad\;2b=a+c$

$b,c,d\;in\;GP\quad\;c^2=bd$

$a+c=2$

$b+d=17$

$a+c=2\quad\;2b=a+c=2$

$b=1$

$b+d=17\quad\;d=17-1=16$

$c^2=bd\quad\;c^2=1*16=16$

$c=\pm4$

$a=2-c$

$=-2\quad\;or\quad\;6$

$Series\;is\;-2,1,4,16\quad\;or\quad\;6,1,-4,16.$

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