there is an obvious pattern. Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8. The common difference is -2, so the formula for the nth term is 12-2(n-1).
This can be written 12-2n+2=14-2n, so that when n=1, the 1st term is 14-2=12.
The 5th term is 14-10=4; the 6th is 14-12=2. And so on. This is the formula The expression for the total number of tiles in the nth term is the sum of the areas of the rectangles, n2 + n(n – 1) + 2, which can be simpli- fied to 2n2 – n + 2. quadratic sequences with visual models these are just examples: The nth odd number is given by the formula 2*n-1.
In linear sequences only, the 'nth-term rule' gives the value of any term in that sequence at position 'n'. It is written as 'xn ± y' where x = the constant difference between term values and y is a particular number. The rule allows you to work out the terms of a sequence. An arithmetic progression is a sequence where each term is a certain number larger than the previous term. The terms in the sequence are said to increase by a common difference, d. For example: 3, 5, 7, 9, 11, is an arithmetic progression where d = 2. The nth term of this sequence is 2n + 1.
