How do you solve 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.

Why is it important to study arithmetic and geometric sequence?

Answer: For me, it’s important to learb the arithmetic and geometric sequence because both of these sequences can be applied in real life. -The arithmetic sequence or sometimes called arithmetic progression is a sequence of numbers in which each consecutive terms have a common difference.

What is the difference between geometric series and geometric sequences?

A geometric sequence is a sequence where the ratio r between successive terms is constant. A geometric series is the sum of the terms of a geometric sequence. The nth partial sum of a geometric sequence can be calculated using the first term a1 and common ratio r as follows: Sn=a1(1−rn)1−r.

Is there a sequence that is both arithmetic and geometric?

Yes, it can both arithmetic and geometric. Now, when d is zero and r is one, a sequence is both geometric and arithmetic. This is because it becomes a (n)=a (1)1 =a (1). It can easily observed that this makes the sequence a constant.

What is the difference between arithmetic and geometric?

The differences between arithmetic and geometric sequences is that arithmetic sequences follow terms by adding, while geometric sequences follow terms by multiplying. The similarities between arithmetic and geometric sequences is that they both follow a certain term pattern that can’t be broken.

What is the formula for arithmetic series?

An arithmetic series is a series whose terms form an arithmetic sequence. We use the one of the formula given below to find the sum of arithmetic series. Sn = (n/2) [2a+ (n-1)d]

Which set of numbers is an arithmetic sequence?

An Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant . For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.