Question

What is the 11th term of the following geometric sequence?
7/9, -7/3, 7, -21, 63..

Answer 1

45,927

Answer 2

\(a_1 = a_1\)

\(a_2 = a_1 \times r\)

\(a_3 = a_2 \times r = a_1 \times r^2\)

\(a_4 = a_3 \times r = a_1 \times r^3\)

\(...\)

\(a_n = a_1 r^{n - 1} \)

\(r = -\dfrac{7}{3} \div \dfrac{7}{9} = -\dfrac{7}{3} \times \dfrac{9}{7} = -3 \)

\(\large a_n = \dfrac{7}{9} \times (-3)^{10 - 1} \)

Answer 3

Last line above should read:

\(\large a_{11} = \dfrac{7}{9} \times (-3)^{11 - 1} \)

Now evaluate this expression to find \(a_{11} \).