Question

20) What is the closed linear form of the sequence 3,4,5,6,7, ...?

A) a= 2n
B) a = 2-n
C) a=3+n
a, = 3-n​

Answer 1

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

`\begin{array}{l}{\text {For } n=0, a=2 *(0)=0} \\\\ {\text {For } n=1, a=2 *(1)=2} \\\\ {\text {For } n=2, a=2 *(2)=4}\end{array}`

We get a sequence 0, 2, 4 which does not satisfy the given sequence

b) a= 2-n

`\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}`

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