Question

How do u write a rule for th sequence to find the unknown term? 56.38, 51.28, 46.18, 41.08

Answer 1

The next term in sequence is 35.98

The rule for nth term of sequence is
`a_n = 56.38 + (n - 1)(-5.1)\\` 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

`51.28 - 56.38 = -5.1\\\\46.18 - 51.28 = -5.1\\\\41.08-46.18 = -5.1`

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:

`a_n = a_1 + (n-1)d`

Where,

`a_n` = nᵗʰ term in the sequence

`a_1` = the first term in the sequence

d = the common difference between terms

Here in this sequence

`a_1 = 56.38`

d = -5.1

Therefore,

`a_n = 56.38 + (n - 1)(-5.1)\\`

Where, n > 0 ( n =1, 2, 3, ....)

Thus the rule to find nth term is found