Question

HELP ASAP!!

1. Consider the sequence
4, -12, 36, -108

Part A: Identify whether the function is an arithmetic sequence or a geometric
sequence and justify your answer.

Part B: Write an explicit formula that could be used to find any term in the
sequence.

Part C: Write a recursive formula for the sequence.

Part D: What is the 9th term in the sequence?

Answer 1

`\underline{\boxed{Part \: A}}: \\ \: \\the \: function \: is \: a \: \boxed{ geometric \: sequence} \\ \\ \underline{\boxed{Part \: B}}: \\\boxed{T_n = a( {r})^((n - 1))} \\ \\ \underline{\boxed{Part \: C}}: \\ \boxed{T_4 = T_3( { - 3})^((1))} \\ \\ \underline{\boxed{Part \: D}}: \\ \boxed{ T_9 = 26,244}`

Explanation:

`\underline{\boxed{Part \: A}}: \\ \: \\the \: function \: is \: a \: \boxed{ geometric \: sequence} \\ this \: due \: to \: their \: common \: ratio (r)= \boxed{- 3} \\ \\ \underline{\boxed{Part \: B}}: \\ \\ let \: the \: required \: term \: be \to \: T_n \\ let \: the \: first \: term \: be \to \: a \\ let \: the \:common \: ratio \: be \to \: r \\ hence : \boxed{T_n = a( {r})^((n - 1))} \\ where \: n \: is \: the \: number \: of \: term. \\ \\ \underline{\boxed{Part \: C}}: \\ let \: the \: required \: term \: be \to \: T_4 \\ hence : \boxed{T_4 = T_3( { - 3})^((1))} \\ \\ \underline{\boxed{Part \: D}}: \\if \: a = 4 : r = ( - 3) : n = 9 \\ hence : \boxed{T_9 = 4( { - 3})^((9 - 1))} \\ hence : \boxed{T_9 = 4( { - 3})^((8))} \\T_9 = 4( 6,561) \\ \boxed{ T_9 = 26,244}`