For a given geometric sequence, the 5th term, a5, is equal to 2327, and the 9th term, a9, is equal to 69. Find the value of the 11th term, a11. If applicable, write your answer as a fraction.

Answer 1

a5 = 2327

a9 = 69

a11 = ?

an = a1(r)^(n-1) where a1 = 1st term, r = the common ratio, n= the nth term

a5 = a1(r)^(4) = 2327

a9 = a1(r)^8 = 69

a1(r)^8/a1(r)^4) = 69/2327

r^4 = 69/2327

r = the fourth root of 69/2327 = about 0.415

a1 = 2327/r^4 = 2327^2/69 = 78,477.2

a11 = a1(r)^10 = (2327^2/69)(69/2327)^2.5 = 69sqr69/sqr2327 = about 11.88

a1 = about 78477

a2 = about 32568

a3 = about 13515

a4 = about 5609

a5 = 2327

a6 = about 966

a7 = about 401

a8 = about 166

a9 = 69

a10 = 29

a11 = about 11.9