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Answer :
Sure! Let's work through the problem step by step to understand how the sequence is generated.
1. Understanding the Function:
Here, we are given a function that generates a sequence, where each term is derived from the previous term by the formula [tex]\( f(x+1) = f(x) - 2 \)[/tex].
2. Starting Value:
We have the initial condition [tex]\( f(1) = 10 \)[/tex]. This means the first term of our sequence is 10.
3. Generating the Sequence:
- First Term:
The first term is given as 10.
- Second Term:
To find the second term, we use the formula:
[tex]\( f(2) = f(1) - 2 = 10 - 2 = 8 \)[/tex]
- Third Term:
For the third term:
[tex]\( f(3) = f(2) - 2 = 8 - 2 = 6 \)[/tex]
- Fourth Term:
For the fourth term:
[tex]\( f(4) = f(3) - 2 = 6 - 2 = 4 \)[/tex]
- Fifth Term:
Finally, for the fifth term:
[tex]\( f(5) = f(4) - 2 = 4 - 2 = 2 \)[/tex]
4. The Complete Sequence:
By applying the formula to each term, the sequence we get is:
[tex]\[ [10, 8, 6, 4, 2] \][/tex]
This sequence follows the pattern of subtracting 2 from the previous term, starting from the initial value of 10.
1. Understanding the Function:
Here, we are given a function that generates a sequence, where each term is derived from the previous term by the formula [tex]\( f(x+1) = f(x) - 2 \)[/tex].
2. Starting Value:
We have the initial condition [tex]\( f(1) = 10 \)[/tex]. This means the first term of our sequence is 10.
3. Generating the Sequence:
- First Term:
The first term is given as 10.
- Second Term:
To find the second term, we use the formula:
[tex]\( f(2) = f(1) - 2 = 10 - 2 = 8 \)[/tex]
- Third Term:
For the third term:
[tex]\( f(3) = f(2) - 2 = 8 - 2 = 6 \)[/tex]
- Fourth Term:
For the fourth term:
[tex]\( f(4) = f(3) - 2 = 6 - 2 = 4 \)[/tex]
- Fifth Term:
Finally, for the fifth term:
[tex]\( f(5) = f(4) - 2 = 4 - 2 = 2 \)[/tex]
4. The Complete Sequence:
By applying the formula to each term, the sequence we get is:
[tex]\[ [10, 8, 6, 4, 2] \][/tex]
This sequence follows the pattern of subtracting 2 from the previous term, starting from the initial value of 10.
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