QuestionFind the first four terms of the sequence defined below, where represents the position of a term in the sequence. Start with .
Studdy Solution
STEP 1
What is this asking?
We need to find the first four terms of a sequence, which means plugging in and into the given formula and calculating the results.
Watch out!
Don't forget that starts at **1**, not **0**!
Also, pay close attention to the order of operations (PEMDAS/BODMAS) when calculating each term.
STEP 2
1. Calculate the first term ().
2. Calculate the second term ().
3. Calculate the third term ().
4. Calculate the fourth term ().
STEP 3
Let's **kick things off** by finding the first term, which means plugging in into our formula.
So, we have .
STEP 4
First, we **square the 1**: .
Now, our equation looks like this: .
STEP 5
Next, we **multiply**: and .
So, we have .
STEP 6
Finally, we **subtract** from left to right: , and then .
Therefore, !
STEP 7
Now, let's **crank out** the second term by plugging in : .
STEP 8
We **square the 2**: , giving us .
STEP 9
**Multiply**: and .
Now, we have .
STEP 10
**Subtract** from left to right: , and then .
So, !
STEP 11
Time for the third term!
Plug in : .
STEP 12
**Square the 3**: , so .
STEP 13
**Multiply**: and , giving us .
STEP 14
**Subtract** from left to right: , and then .
So, !
STEP 15
Last one!
Let's find the fourth term with : .
STEP 16
**Square the 4**: , so .
STEP 17
**Multiply**: and , giving us .
STEP 18
**Subtract** from left to right: , and then .
Therefore, !
STEP 19
The first four terms of the sequence are , , , and .
Was this helpful?