Q:

How do you find the nth term of a sequence of numbers?

A:

In a sequence of numbers, each successive term is usually obtained by adding a certain fixed number to the previous term of the sequence. The equation to calculating the nth term of the sequence is an+b; "a" is the fixed number that is being added to generate the series, and "b" gives the relation between the fixed number and the first number of the sequence.

For a series of numbers, each successive number is calculated by adding a certain fixed value to the previous number of the series. For example, in the series 6,10,14,18, the number 4 is added to each term. In this example, a=4, so for this series, the equation is written as 4n+b.

The fixed value is 4, and the first term of the series is 6. To solve the equation, find the relation between the fixed number and the first number of the sequence. To obtain the first term from the fixed value, 2 must be added to the fixed value. This gives the relationship between the two, thus completing the equation as 4n+2. Using this equation, the fourth term of the series would be 4(4)+2, which is 18, the 25th term of the equation would be 4(25)+2, which is 102, and so on.


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