A geometric sequence is defined recursively by an=4a(small n-1). the first term of the sequence is 0.5. What is the explicit formula for the nth term of the sequence?

Question

hartnn · Answer

to get explicit formula you will need 2 terms, a1 = first term
and r = common ratio
know how to get any of these ?

anonymous · Answer

r is just u can take the 2nd term over the first term..

hartnn · Answer

oops, a1 = 0.5 is given :P
know how to get r ?

anonymous · Answer

but idk how to find ratio out of a formula & yea a1 is given

hartnn · Answer

yes, or you can say any next term to current term like 
 $\huge r=a_n/a_{n-1}$

hartnn · Answer

so, here r= .... ?

anonymous · Answer

so is the answer:
a_n= 0.5*4^n-1???

hartnn · Answer

did you get how ? do you want to know how ?

anonymous · Answer

well the explicit 4mula for a geometric sequence is:
a_n= a1*r^(n-1)..

hartnn · Answer

yes, a1 = 00.5
just need to find r, thats what i was explaining...

hartnn · Answer

that how is r=4

anonymous · Answer

wait but how can u find the ratio using that 4mula?

hartnn · Answer

$\huge r=a_n/a_{n-1}$

and an = 4 a(n-1) is given

anonymous · Answer

ok so my ans is correct right?

hartnn · Answer

yup.

anonymous · Answer

ok

anonymous · Answer

yea?

anonymous · Answer

no don't take it like that... just leave it

anonymous · Answer

its fine rishab...  just leave it ok

rishabh.mission · Answer

ok then God bye :)

anonymous · Answer

bye

hartnn · Answer

now that rishabh has deleted his comments, this conversation sounds weird to me :P

anonymous · Answer

he deleted his comments?

anonymous · Answer

oh wait, yeah i guess so too...

rishabh.mission · Answer

don't guess its real.... lol

anonymous · Answer

no really?

rishabh.mission · Answer

yes :)