The rule to get from one term to the next in a sequence is x_(n+1)=3x_(n)+8 If x_(1)=4 work out the value of x_(3)

Question

Question

The rule to get from one term to the next in a sequence is x_(n+1)=3x_(n)+8 If x_(1)=4 work out the value of x_(3)

Answer 1

To begin with, for \( x _ { 2 } \): \[ x _ { 2 } = 3 x _ { 1 } + 8 = 3(4) + 8 = 20 \] Then for \( x _ { 3 } \): \[ x _ { 3 } = 3 x _ { 2 } + 8 = 3(20) + 8 = 68 \] Therefore, the value of \( x_{3} \) equals 68.

Answer 2

## Step1: Identify the recursive formula given in the problem which defines the steps to get from one term to another. ***The recursive formula here is:*** \(x _ { n + 1 } = 3 x _ { n } + 8\). ## Step2: From step1, we realize that to evaluate \(x _ { 3 } \), we have to calculate \( x_{2}\) first. Plug \( n = 1 \) (since given \( x_{1} \)) into the recursive formula. ### The formula applied here for first calculation is \( x _ { 1+1 } = 3 x _ { 1 } + 8 \). ## Step3: Calculate based on this formula. Given that \( x_{1} = 4 \), substitute it into the above formula to find \( x_{2} \). After obtaining \( x_{2} \), use this \( x_{2} \) to calculate \( x_{3} \). ### The formula applied here for second calculation is\( x _ { 2+1 } = 3 x _ { 2 } + 8 \). By substitution using multiple steps, step-by-step, and performing the arithmetical operation, \( x _ { 3 } \) can be obtained.

Question

The rule to get from one term to the next in a sequence is x_(n+1)=3x_(n)+8 If x_(1)=4 work out the value of x_(3)

Answer

Answer

Explain

Hot Questions