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.
Know MoreFor 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.
Learn more about ArithmeticAn arithmetic sequence is a sequence of numbers where there is a definitive pattern between the consecutive terms of the series. In general, arithmetic sequences can be represented by x = a + d(n - 1).
Full Answer >The next number in this sequence is 24. This would follow the pattern of adding five to a number and then subtracting two. The first three numbers of this sequence indicate this: 13 + 5 = 18 and 18 - 2 = 16.
Full Answer >The associative property of multiplication states that the order in which numbers are multiplied in sequence is irrelevant. In other words, if more than two numbers in an expression are multiplied together, the product is the same no matter the order in which the numbers are multiplied.
Full Answer >The term "PEMDAS" can be remembered through several expanded versions including "Please Excuse My Dear Aunt Sally," "Pudgy Elves May Demand a Snack," "Popcorn Every Monday Donuts Always Sunday," "Please Eat Mom's Delicious Apple Strudels" and "People Everywhere Made Decisions About Sums." It is used as a mnemonic device for the order of operations.
Full Answer >