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;
\(d=a_{n+1} - a_n\) for all n∈N
Given sequence:- 1.31, 2.54 , 3.77 , ___ ;
we have;
\(a_1 = 1.31\) , \(a_2= 2.54\) and \(a_3 = 3.77\)
First find the common difference;
\(d =a_2 - a_1\) = \(2.54-1.31 = 1.23\)
or
d = \(=a_3-a_2 = 3.77-2.54 =1.23\)
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;
\(a_4 = 3.77+1.23 = 5.00\)
Therefore, in the given sequence next term will be 5.00.
