An 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).
Arithmetic formulas originate from the need to determine the value or position of a specific term within an arithmetic sequence, where the difference between successive terms is a constant d, such as "an = a1 - (n - 1)d." Geometric formulas are derived from a similar ne...
Calculate the sum of an arithmetic sequence with the formula (n/2)(2a + (n-1)d). The sum is represented by the Greek letter sigma, while the variable a is the first value of the sequence, d is the difference between values in the sequence, and n is the number of terms i...
To calculate geometric mean for a set of numbers, multiply the numbers together, and take the nth root of this product. Only calculate the geometric mean when all of the numbers in a set are nonzero and positive.
Arithmetic sequences are used in daily life for different purposes, such as determining the number of audience members an auditorium can hold, calculating projected earnings from working for a company and building wood piles with stacks of logs. Arithmetic sequences are...
There are many uses of geometric sequences in everyday life, but one of the most common is in calculating interest earned. Mathematicians calculate a term in the series by multiplying the initial value in the sequence by the rate raised to the power of one less than the...
The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1). The variable a_n is equal to the value of the nth term in the given geometric sequence, while a_1 is the value of the first term in the sequence.