Answer :
Answer:
171,
Step-by-step explanation:
We have the sequence 1 , 3 , 11 , 43 , __.
Let us say [tex]a_{1}=1[/tex] , [tex]a_{2}=3[/tex] , [tex]a_{3}=11[/tex] , [tex]a_{4}=43[/tex] and it is required to find out [tex]a_{5}[/tex].
As, we can see the pattern from the given four terms that,
[tex]a_{2}=a_{1}+2[/tex] i.e. [tex]a_{2}=a_{1}+2^{1}[/tex]
[tex]a_{3}=a_{2}+8[/tex] i.e. [tex]a_{3}=a_{1}+2^{3}[/tex]
[tex]a_{4}=a_{3}+32[/tex] i.e. [tex]a_{4}=a_{1}+2^{5}[/tex]
Since, the next term is obtained by adding the previous terms by odd powers of two.
Therefore, [tex]a_{5}=a_{4}+2^{7}[/tex] i.e. [tex]a_{5}=a_{4}+128[/tex] i.e [tex]a_{5}=43+128[/tex] i.e. [tex]a_{5}=171[/tex]
So, [tex]a_{5}=171[/tex].
Hence, the next term of the sequence is 171.
The numbers follow a sequence.
The next number in the sequence is 171
The sequence is given as:
[tex]\mathbf{Sequence = 1, 3, 11, 43, .....}[/tex]
So, we have:
[tex]\mathbf{T_1= 1}[/tex]
[tex]\mathbf{T_2= 3}[/tex]
[tex]\mathbf{T_3= 11}[/tex]
[tex]\mathbf{T_4= 43}[/tex]
Rewrite as:
[tex]\mathbf{T_2 = 1 + 2}[/tex]
[tex]\mathbf{T_3 = 3 + 8}[/tex]
[tex]\mathbf{T_4 = 11 + 32}[/tex]
Rewrite as:
[tex]\mathbf{T_2 = T_1 + 2}[/tex]
[tex]\mathbf{T_3 = T_2 + 8}[/tex]
[tex]\mathbf{T_4 = T_3 + 32}[/tex]
Express as a power of 2
[tex]\mathbf{T_2 = T_1 + 2^1}[/tex]
[tex]\mathbf{T_3 = T_2 + 2^3}[/tex]
[tex]\mathbf{T_4 = T_3 + 2^5}[/tex]
So, the next term is: have:
[tex]\mathbf{T_5 = T_4 + 2^7}[/tex]
Substitute 43 for T4
[tex]\mathbf{T_5 = 43 + 2^7}[/tex]
[tex]\mathbf{T_5 = 43 + 128}[/tex]
[tex]\mathbf{T_5 = 171}[/tex]
Hence, the next number in the sequence is 171
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