Question

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

begin at term a0 and have a2 = 4 and a4 = 12.

Answer 1

Answer:-288

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* 4=36`

For GP

`4=a_0r^2`----3

`12=a_0r^4`----4

From 3 & 4 we get

`3=r^2`

`r=√(3)`

`a_0=(4)/(3)`

For
`a_(10)=(4)/(3)* 3^5=324`

`AP_{a_(10)}-GP_{a_(10)}=36-324=-288`