The next term in sequence is 35.98
The rule for nth term of sequence is [tex]a_n = 56.38 + (n - 1)(-5.1)\\[/tex] Where, n > 0 ( n =1, 2, 3, ....)
Solution:
Given sequence is:
56.38, 51.28, 46.18, 41.08
Let us first find the difference between the terms
[tex]51.28 - 56.38 = -5.1\\\\46.18 - 51.28 = -5.1\\\\41.08-46.18 = -5.1[/tex]
Thus the difference between next term and previous term is same
Next term will be,
41.08 - 5.1 = 35.98
Thus the next term in sequence is 35.98
Therefore, the sequence is arithmetic sequence
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant
The formula for nth term of arithmetic sequence is given as:
[tex]a_n = a_1 + (n-1)d[/tex]
Where,
[tex]a_n[/tex] = nᵗʰ term in the sequence
[tex]a_1[/tex] = the first term in the sequence
d = the common difference between terms
Here in this sequence
[tex]a_1 = 56.38[/tex]
d = -5.1
Therefore,
[tex]a_n = 56.38 + (n - 1)(-5.1)\\[/tex]
Where, n > 0 ( n =1, 2, 3, ....)
Thus the rule to find nth term is found
