What is the 6th term in the geometric sequence where a1= 1,024 and a4= -16? Can anybody solve this problem please ?

Question

hartnn · Answer

yes, do u know the basic formulas for geometric sequence ?

anonymous · Answer

no :( unfortunately this make up work from school and i missed the notes for that day.

hartnn · Answer

ok, the 'n' th term of a geometric sequence is given by 
$\huge T_n=a_1r^{n-1}$
where a1 is first term and r is common ratio.

hartnn · Answer

based on this formula, and using a4 = -16 , can u find r ?

hartnn · Answer

$\huge a_n=a_1r^{n-1}$

anonymous · Answer

i think soo but this is all starting to make more sense.

hartnn · Answer

yes, in that formula just put n=4, a4=-16, a1 = 1024 
and get the value of r

anonymous · Answer

okayy then what would i do after that could you guide me through this please

anonymous · Answer

@hartnn

hartnn · Answer

yes, first find the value of r using that formula and tell me what u get ?

anonymous · Answer

okay

anonymous · Answer

for the answer i got -0.25

hartnn · Answer

thats correct, r = -0.25 
now use the same formula to get 6th term
here n= 6
a1 = 1024 , r = -0.25

anonymous · Answer

i got -1

hartnn · Answer

correct! 
so, sixth term = -1
clear with all steps ?

hartnn · Answer

anonymous · Answer

yes thank you for the guidance it feels good to solve the problem :)

hartnn · Answer

welcome ^_^