Answer:-288
Step-by-step explanation:
Given
First term [tex]a_0[/tex] is common for both AP and GP
For AP
[tex]a_2=4=a_0+2d[/tex]---1
[tex]a_4=12=a_0+4d[/tex]----2
From 1 & 2 we get
d=4
[tex]a_0=-4[/tex]
[tex]a_{10}[/tex] for AP
[tex]a_{10}=a_0+10d=-4+10\times 4=36[/tex]
For GP
[tex]4=a_0r^2[/tex]----3
[tex]12=a_0r^4[/tex]----4
From 3 & 4 we get
[tex]3=r^2[/tex]
[tex]r=\sqrt{3}[/tex]
[tex]a_0=\frac{4}{3}[/tex]
For [tex]a_{10}=\frac{4}{3}\times 3^5=324[/tex]
[tex]AP_{a_{10}}-GP_{a_{10}}=36-324=-288[/tex]
