Question

5) Given the explicit formula for a geometric sequence find the first five terms and then-1gth term. PAM.NLF.1 ,,= 3a) first 5 terms:b) 8th term:I[

Answer 1

a)

$\begin{gathered} g_{_1\text{ }}=3^{1-1^{}\text{ }}=3^0=1\text{ } \\ g_{2\text{ }}=3^{2-1\text{ }}=3^1\text{ = 3} \\ g_3=3^{3-1}=3^2\text{ = 9} \\ g_4=3^{4-1}=3^3\text{ = 27} \\ g_5=3^{5-1\text{ }}=3^4\text{ = 81} \end{gathered}$

first five terms = 1, 3, 9, 27, 81

b)

$g_{8_{\text{ }}}=3^{8-1}=3^7\text{ = 2187}$