# Given the explicit formula for a geometric sequence find the first five terms and the 8th term

7) a_n = 3^(n − 1)
8) a_n = 2 ⋅ (1/4)^(n − 1)
9) an = −2.5 ⋅ 4^(n − 1)
10) an = −4 ⋅ 3^(n-1)

7)
a_n  =  3^(n − 1)
a1  =  3^(1 − 1)
=  3^(0)
=  1
a2  =  3^(2 − 1)
=  3^(1)
=  3
a3  =  3^(3 − 1)
=  3^(2)
=  9
a4  =  3^(4 − 1)
=  3^(3)
=  27
a5  =  3^(5 − 1)
=  3^(4)
=  81
a8  =  3^(8 − 1)
=  3^(7)
=  2187

8)
a_n  =  2 X (1/4)^(n − 1)
a1  =   2 X (1/4)^(1 − 1)
=  2 X (1/4)^(0)
=  2
a2  =   2 X (1/4)^(2 − 1)
=  2 X (1/4)^(1)
=  2 X (1/4)
=  1/2
a3  =   2 X (1/4)^(3 − 1)
=  2 X (1/4)^(2)
=  2 X (1/16)
=  1/8
a4  =   2 X (1/4)^(4 − 1)
=  2 X (1/4)^(3)
=  2 X (1/64)
=  1/32
a5  =   2 X (1/4)^(5 − 1)
=  2 X (1/4)^(4)
=  2 X (1/256)
=  1/128
a8  =   2 X (1/4)^(8 − 1)
=  2 X (1/4)^(7)
=  2 X (1/16384)
=  1/8192

Contd........

9)

an  =  −2.5 ⋅ 4^(n − 1)
a1  =  −2.5 ⋅ 4^(1 − 1)
=  −2.5 ⋅ 4^(0)
=  -2.5
a2  =  −2.5 ⋅ 4^(2 − 1)
=  −2.5 ⋅ 4^(1)
=  -2.5 X 4
=  -10
a3  =  −2.5 ⋅ 4^(3 − 1)
=  −2.5 ⋅ 4^(2)
=  -2.5 X 16
=  -40
a4  =  −2.5 ⋅ 4^(4 − 1)
=  −2.5 ⋅ 4^(3)
=  -2.5 X 64
=  -160
a5  =  −2.5 ⋅ 4^(5 − 1)
=  −2.5 ⋅ 4^(4)
=  -2.5 X 256
=  -640
a8  =  −2.5 ⋅ 4^(8 − 1)
=  −2.5 ⋅ 4^(7)
=  -2.5 X 16384
=  -40960

10)
an = −4 ⋅ 3^(n-1)
a1  =  -4 X 3^(1 − 1)
=  -4 X 3^(0)
=  -4
a2  =  -4 X 3^(2 − 1)
=  -4 X 3^(1)
=  -4 X 3
=  -12
a3  =  -4 X 3^(3 − 1)
=  -4 X 3^(2)
=  -4 X 9
=  - 36
a4  =  -4 X 3^(4 − 1)
=  -4 X 3^(3)
=  -4 X 27
=  -108
a5  =  -4 X 3^(5 − 1)
=  -4 X 3^(4)
=  -4 X 81
=  - 324
a8  =  -4 X 3^(8 − 1)
=  -4 X 3^(7)
=  -4 X 2187
=  - 8748