Question

What's the pattern of 101,94,87,80

Answer 1

Arithmetic sequence states that it is a sequence of numbers such that the difference of any two successive members of the sequence is a constant(d)

The rule for the sequence is:

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

where a is the first term , d is the common difference and n is the number of terms.

Given the pattern: 101, 94, 87, 80.

First term (a) = 101

This pattern is an arithmetic sequence with common difference(d) = -7

Since,

94 -101 = -7

87 -94 = -7

80- 87 = -7

The rule for this pattern is;

`a_n = 101+(n-1)(-7)= 101 -7n + 7`

or

`a_n = 108 -7n`

Therefore, the rule for this pattern is,
`a_n = 108 -7n` where n is the number of term.