write an expression to describe the rule for the pattern. 1, 4, 13, 40, 121, ...
It is a linear sequence so we use a$d,since d=3 $a=1 depending on the terms,it increases by;a+(d raise to power N-1)
Look at the difference
3 9 27 81
first term = 1
First term plus 3 3^1 = 4
second term plus 9 3^2 = 13
third term plus 27 3^3
fourth term plus 81 3^4
Can you write an expression for this. If you let term # = n
Sorry,they increase by the addition of their preceding term to D raise to power N-2
To describe the rule for the pattern 1, 4, 13, 40, 121, ..., we can observe that each term is obtained by multiplying the previous term by 3 and then subtracting 2.
Using this information, we can write an expression to describe the pattern:
1st term: 1
2nd term: (1 * 3) - 2 = 1
3rd term: (4 * 3) - 2 = 10
4th term: (13 * 3) - 2 = 37
5th term: (40 * 3) - 2 = 118
So, the expression to describe the pattern is:
n^th term = (n-1) * 3 - 2, where n is the position of the term in the pattern.