Answer:
Option B is correct
For [tex]n\geq 1[/tex] , the function for the given sequence is defined as; [tex]f[n] = 4 +3n[/tex]
Step-by-step explanation:
An arithmetic sequence is a sequence in which the difference between each consecutive term is constant.
An explicit formula for this arithmetic sequence given by;
[tex]a_n = a+(n-1)d[/tex] where a represents first term
Since, the given sequences; 7 , 10 , 13 , 16 and 19
⇒ common difference(d) = 3 and a = 7
Since.
10 -7 = 3
13- 10 = 3 ....
The function which defined this sequence is;
[tex]f[n]=a_n = 7 +(n-1)(3)[/tex]
using distributive property:
[tex]f[n] = 7 + 3n -3[/tex]
[tex]f[n] = 4 +3n[/tex]
therefore, the function for the given sequence for all integers [tex]n\geq 1[/tex] is; [tex]f[n] = 4 +3n[/tex]
The correct option is D) f(n) = 4 + 3n.
Step-by-step explanation:
Given :
Arithmetic Sequence -- 7,10,13,16,19
Solution :
The explicit formula of arithmetic sequence is given by,
[tex]T_n = a+(n-1)d[/tex] ------- (1)
where, common difference (d) = 10 - 7 = 3
first term (a) = 7
So from equation (1),
[tex]T_n = 7+(n-1)3 = 7+3n-3[/tex]
[tex]T_n = 4 + 3n[/tex]
Therefore, the correct option is D) f(n) = 4 + 3n.
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https://brainly.com/question/15412619?referrer=searchResults
