Geo sequence 1 and 2

Question

Consider the sequence 3, -9, 27, -81, ...

Part A: Write an explicit formula for the sequence.

Part B: Write a recursive formula for the sequence.

Part C: Find the 14th term of the sequence.

Consider the sequence 7, 21, 63, 189, 567 …

Part A: Write an explicit formula for the sequence.

Part B: Write a recursive formula for the sequence.

Part C: Find the 9th term of the sequence.

Answer 1

1) Common ratio r = -3, a₁= 3

A) a_n= a₁r^n-1 = 3(-3)^n-1

B) a_n= a_n-1r = -3a_n-1

C) a₁₄=3(-3)¹³=-3¹⁴=4782969

2) Common ratio r = 3, a₁ = 7

A) a_n=7(3)^n-1

B) a_n=3a_n-1

C) a₉=7(3)⁸= 7(6561) = 45927