Respuesta :
The closed linear form of sequence 3, 4, 5, 6, 7, .. is a = 3 + n
Option C
Solution:
Given Sequence is 3, 4, 5, 6, 7, ...
Let us the check the each option which can form the above sequence
a) a= 2n
[tex]\begin{array}{l}{\text {For } n=0, a=2 \times(0)=0} \\\\ {\text {For } n=1, a=2 \times(1)=2} \\\\ {\text {For } n=2, a=2 \times(2)=4}\end{array}[/tex]
We get a sequence 0, 2, 4 which does not satisfy the given sequence
b) a= 2-n
[tex]\begin{array}{l}{\text {For } n=0, a=2-0=2} \\\\ {\text {For } n=1, a=2-1=1} \\\\ {\text {For } n=2, a=2-2=0}\end{array}[/tex]
We get a sequence 2, 1, 0 which does not satisfy the given sequence
c) a= 3+n
For n = 0, a = 3 + 0 = 3
For n = 1, a = 3 + 1 = 4
For n = 2, a = 3 + 2 = 5
For n = 3 , a = 3 + 3 = 6
For n = 4, a = 3 + 4 = 7
Which satisfy the given sequence
Hence, c) is the correct option
