Answer:
Option B is correct.
the next term of the sequence is 5.00
Explanation:
Arithmetic progression(A.P) is a sequence of numbers in which the consecutive terms are formed by adding a constant quantity with the preceding term.
Common difference(d) is the constant quantity stated in the above definition of arithmetic progression. it is given by;
[tex]d=a_{n+1} - a_n[/tex] for all n∈N
Given sequence:- 1.31, 2.54 , 3.77 , ___ ;
we have;
[tex]a_1 = 1.31[/tex] , [tex]a_2= 2.54[/tex] and [tex]a_3 = 3.77[/tex]
First find the common difference;
[tex]d =a_2 - a_1[/tex] = [tex]2.54-1.31 = 1.23[/tex]
or
d = [tex]=a_3-a_2 = 3.77-2.54 =1.23[/tex]
Therefore, by the definition of arithmetic progression,
the given sequence is Arithmetic progression
Now, to find the fourth term of the sequence, add constant quantity (d) to the third term;
[tex]a_4 = 3.77+1.23 = 5.00[/tex]
Therefore, in the given sequence next term will be 5.00.
