What is the 7th term of the geometric sequence where a1 = -2 and a5 = -512?

Question

1434 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-06T14:45:42

#q = + 4 Rightarrow a_6 = - 2048#
#q = - 4 Rightarrow a_6 = + 2048#

#a_n = a_0 * q^n#

#a_1 = a_0 q = -2#

#a_5 = a_0 q^5 = -512#

#a_5/ a_1 = q^4 = frac{-512}{-2} = 256 = 2^8#

#q = ± 4#

#a_1 = a_0 (±4) = -2 Rightarrow a_0 = ± (- 1/2)#

#a_6 = a_5 * q = -512 * (±4) = ± (- 2048) #