Identify the 16th term of a geometric sequence where a1 = 4 and a8 = -8,748

Question

hartnn · Answer

do you know the formula for n'th term of geometric sequence ?

anonymous · Answer

an= a1 x r ^n-1

hartnn · Answer

correct! 

now put n= 8 there....
a8 is -8748
n=8, a1 =4

only 'r' is unknown, can you find it ?

anonymous · Answer

how do you find the r ?

anonymous · Answer

can you please help me find the 16th term though

hartnn · Answer

-8748 = 4 8 r^7 

once you get the value of common ratio 'r' 
finding the 16th term is just one step! :)

hartnn · Answer

***  -8748 = 4 *r^7 

can you find r from here ?

anonymous · Answer

no can you help me please

hartnn · Answer

-8748 = 4 *r^7 

divide both sides by 4
what u get ?

anonymous · Answer

is it -2187 = xx ^n-7

hartnn · Answer

-2187 = r^7

now use the calculator to get 7th root of 2187

anonymous · Answer

is ir 46.7653718

hartnn · Answer

no, its simply -3
because -3^7 = -2187

hartnn · Answer

now we have r=-3 
and we need 16th term,
so we put n=16
and plug these in the n'th term equation, 
an= a1 x r ^n-1

hartnn · Answer

a16 = 4 (-3)^15 = ... ?

anonymous · Answer

is it -8748

hartnn · Answer

no, just use a calculator to calculate 
4*(-3)^15

anonymous · Answer

yea thank you i got it