Q:

20) What is the closed linear form of the sequence 3,4,5,6,7, ...?A) a= 2nB) a = 2-nC) a=3+na, = 3-n​

Accepted Solution

A:
The closed linear form of sequence 3, 4, 5, 6, 7, .. is a = 3 + nOption CSolution:Given Sequence is 3, 4, 5, 6, 7, ...Let us the check the each option which can form the above sequencea) 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 sequenceb) 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 sequencec) a= 3+nFor n = 0, a = 3 + 0 Β = 3For n = 1, a = 3 + 1 Β = 4For n = 2, a = 3 + 2 = 5For n = 3 , a = 3 + 3 = 6For n = 4, a = 3 + 4 = 7Which satisfy the given sequenceHence, c) is the correct option