Question

Find the difference between the terms a10 of an arithmetic sequence and a geometric sequence, both of which

Answer 1

Answer:-288

Step-by-step explanation:

Given

First term $a_0$  is common for both AP and GP

For AP

$a_2=4=a_0+2d$---1

$a_4=12=a_0+4d$----2

From 1 & 2 we get

d=4

$a_0=-4$

$a_{10}$ for AP

$a_{10}=a_0+10d=-4+10\times 4=36$

For GP

$4=a_0r^2$----3

$12=a_0r^4$----4

From 3 & 4 we get

$3=r^2$

$r=\sqrt{3}$

$a_0=\frac{4}{3}$

For $a_{10}=\frac{4}{3}\times 3^5=324$

$AP_{a_{10}}-GP_{a_{10}}=36-324=-288$