Question

6, 11, 31, 121, 601, ?
A.3600
B.3621
C.3601
D.3611

Answer 1

this is the solution of this question

Answer 2

Answer:

Concept:

Sequence:

• In mathematics, a sequence is a list of elements, typically numbers, where the order of the elements is significant.
• In this case, everything fits into a predetermined pattern.
• 1,2,3,... is an example of Infinite sequence.
• 6,11,31,121,601,x is a finite sequence.

Step-by-step explanation:

Given:

The given sequence is $6, 11, 31, 121, 601, ?$

To Find:

We need to find the next number of the given sequence.

Solution:

let us consider term 6 be x.

$Term1=6$

$Term2=11$

$Term3=31$

$Term4=121$

$Term5 = 601$

$Term 6 =x$

Let T1 be the term 1, T2 be the term 2,T3 be the term 3, T4 be the term 4, T5 be the term 5 and T6 be the term 6 respectively.

$T_{2}=(T_{1}*2)-1 = (6*2)-1 =12-1=11$

$T_{3}=(T_{2}*3)-2 = (11*3)-2 =33-2=31$

$T_{4}=(T_{3}*4)-3 = (31*4)-3 =124-3=121$

$T_{5}=(T_{4}*5)-4 = (121*5)-4 =605-4=601$

The given sequence is in the form of,

$T_{n}=(T_{n-1}*n)-(n-1)$

Now we need to find the term 6, so substitute $n=6$ in the above equation,

$T_{6}=(T_{6-1}*6)-(6-1)$

$T_{6}=(T_{5}*6)-(5)$

Substitute $T_{5} =601$,

$T_{6}=(601*6)-(5)$

$T_{6}=3606-5$

$T_{6}=3601$

Therefore, Sixth term of the given sequence is $3601$, then the sequence will be $6, 11, 31, 121, 601, 3601$.

#SPJ3