What if a sequence is both arithmetic and geometric?

Is it possible for a sequence to be both arithmetic and geometric? Yes, because we found an example above: where c is a constant will be arithmetic with d = 0 and geometric with r = 1. It turns out that this is the only type of sequence which can be both arithmetic and geometric.

How will you find the next in an arithmetic sequence and a geometric sequence?

The common pattern in an arithmetic sequence is that the same number is added or subtracted to each number to produce the next number. The common pattern in a geometric sequence is that the same number is multiplied or divided to each number to produce the next number.

How are geometric and arithmetic sequences alike and different?

An arithmetic sequence is a sequence of numbers that is calculated by subtracting or adding a fixed term to/from the previous term. However, a geometric sequence is a sequence of numbers where each new number is calculated by multiplying the previous number by a fixed and non-zero number.

How are an arithmetic sequence and a geometric sequence alike How are they different?

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms.

How do you solve for the sum of an arithmetic sequence?

An arithmetic sequence is defined as a series of numbers, in which each term (number) is obtained by adding a fixed number to its preceding term. Sum of arithmetic terms = n/2[2a + (n – 1)d], where ‘a’ is the first term, ‘d’ is the common difference between two numbers, and ‘n’ is the number of terms.

How do you know if a sequence is arithmetic?

An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.

How do you write arithmetic and geometric sequences?

An Arithmetic Sequence is such that each term is obtained by adding a constant to the preceding term. This constant is called the Common Difference. Whereas, in a Geometric Sequence each term is obtained by multiply a constant to the preceding term.

How can you determine the common difference of an arithmetic sequence?

The common difference is the value between each successive number in an arithmetic sequence. Therefore, the formula to find the common difference of an arithmetic sequence is: d = a(n) – a(n – 1), where a(n) is the last term in the sequence, and a(n – 1) is the previous term in the sequence.

How are the partial sums of arithmetic series and geometric series different from each other?

An arithmetic series is the sum of the terms of an arithmetic sequence. A geometric series is the sum of the terms of a geometric sequence. The partial sum is the sum of a limited (that is to say, a finite) number of terms, like the first ten terms, or the fifth through the hundredth terms.