Question

I really don’t know what this is. I go to SHSAT prep and I think it’s a subscript. When you explain, pls explain like your teaching a 5 year old

Answer 1

`\textsf{C)} \quad (21)/(5)`

Explanation:

`\Large\textsf{$\sf x_n=x_(n-1)+x_(n-2)$}`

The given formula is a recursive formula, often referred to as a recurrence relation. It is used to generate a sequence of numbers where each term (xₙ) depends on the previous two terms (xₙ₋₁ and xₙ₋₂).

Here is a breakdown of the formula:

• xₙ represents the nth term in the sequence, where n = 0 is the initial term.
• xₙ₋₁ represents the term immediately before the nth term.
• xₙ₋₂ represents the term two positions before the nth term.

To generate the sequence, we need to specify the initial values of x₀ and x₁ because the formula relies on these values to start the sequence.

Given that x₀ = 2 and x₁ = 3, we can generate the next term (x₂) using the formula, as follows:

`\sf x_ 2= x_(2-1) + x_(2-2)`

`\sf x_ 2 = x_1 + x_0`

`\sf x_ 2 = 3 + 2`

`\sf x_ 2 = 5`

To find x₅/x₂, we first need to determine the value of x₅. To do this using the formula, we would need to first calculate x₃ and x₄. However, as the sequence has already been given to us, we can simply find the value of x₅ from the given sequence.

Sequence:

• 2, 3, 5, 8, 13, 21, 34, 55

Therefore:

`\large\begin{array}c\cline{1-8}\vphantom{\frac12}\sf x_0&\sf x_1&\sf x_2&\sf x_3&\sf x_4&\sf x_5&\sf x_6&\sf x_7\\\cline{1-8}\vphantom{\frac12}2&3&5&8&13&21&34&55\\\cline{1-8}\end{array}`

From the table, we can see that x₅ = 21. Therefore, to find x₅/x₂, we can simply divide the corresponding values for those terms:

`\sf (x_5)/(x_2)=(21)/(5)`

Therefore:

`\Large\boxed{\boxed{\sf (x_5)/(x_2)=(21)/(5)}}`