From tech troubles to travel tips, IDNLearn.com has answers to all your questions. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.

Find the first three terms of the sequence defined below, where [tex] n [/tex] represents the position of a term in the sequence. Start with [tex] n = 1 [/tex].

[tex]\[ f(n) = -2n + 7 \][/tex]

[tex]\[
\begin{aligned}
&\text{Term 1: } f(1) = \square \\
&\text{Term 2: } f(2) = \square \\
&\text{Term 3: } f(3) = \square
\end{aligned}
\][/tex]


Sagot :

To find the first three terms of the sequence defined by [tex]\( f(n) = -2n + 7 \)[/tex], we'll follow these steps for [tex]\( n = 1, 2, \)[/tex] and [tex]\( 3 \)[/tex]:

1. Determine the first term ([tex]\( f(1) \)[/tex]):
- Substitute [tex]\( n = 1 \)[/tex] into the function:
[tex]\[ f(1) = -2(1) + 7 \][/tex]
- Perform the multiplication:
[tex]\[ f(1) = -2 \cdot 1 + 7 = -2 + 7 \][/tex]
- Add the results:
[tex]\[ f(1) = 5 \][/tex]


2. Determine the second term ([tex]\( f(2) \)[/tex]):
- Substitute [tex]\( n = 2 \)[/tex] into the function:
[tex]\[ f(2) = -2(2) + 7 \][/tex]
- Perform the multiplication:
[tex]\[ f(2) = -2 \cdot 2 + 7 = -4 + 7 \][/tex]
- Add the results:
[tex]\[ f(2) = 3 \][/tex]


3. Determine the third term ([tex]\( f(3) \)[/tex]):
- Substitute [tex]\( n = 3 \)[/tex] into the function:
[tex]\[ f(3) = -2(3) + 7 \][/tex]
- Perform the multiplication:
[tex]\[ f(3) = -2 \cdot 3 + 7 = -6 + 7 \][/tex]
- Add the results:
[tex]\[ f(3) = 1 \][/tex]

Thus, the first three terms of the sequence are:
[tex]\[ 5, 3, 1 \][/tex]