How do you find the nth term of the geometric sequence given a3=9 r=-1/2 and n=7 ?

Question

1288 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-30T03:49:09

#color(brown)(a_7 = 9/16#

#n^th " term of a geometric sequence is given by the formula "

#a_n = a * r^(n-1), "where 'a' the first term, 'r' common ratio"#

#"Given : a_3 = 9, r = -1/2, n = 7#

#a_3 = 9 = a * (-1/2)^(3-1) = a * (-1/2)^2 = a / 4#

#a = 9 * 4 = 36#

#:. a_n = a * r^(n-1) = 36 * (-1/2)^(7-1) = 36 * (-1/2)^6#

#a_7 = 36 * (1/64) = 36/64 = 9/16#