write down the 10 th term of given pattern 7x+20
Answers
Answer:
Logo
NOV 21, 2020
How to Find the General Term of Sequences
RAY
Ray is a licensed engineer in the Philippines. He loves to write about mathematics and civil engineering.
What Is a Sequence?
A sequence is a function whose domain is an ordered list of numbers. These numbers are positive integers starting with 1. Sometimes, people mistakenly use the terms series and sequence. A sequence is a set of positive integers while series is the sum of these positive integers. The denotation for the terms in a sequence is:
a1, a2, a3, a4, an, . . .
Finding the nth term of a sequence is easy given a general equation. But doing it the other way around is a struggle. Finding a general equation for a given sequence requires a lot of thinking and practice but, learning the specific rule guides you in discovering the general equation. In this article, you will learn how to induce the patterns of sequences and write the general term when given the first few terms. There is a step-by-step guide for you to follow and understand the process and provide you with clear and correct computations.
ADVERTISING
General Term of Arithmetic and Geometric Series
General Term of Arithmetic and Geometric Series
John Ray Cuevas
What Is an Arithmetic Sequence?
An arithmetic series is a series of ordered numbers with a constant difference. In an arithmetic sequence, you will observe that each pair of consecutive terms differs by the same amount. For example, here are the first five terms of the series.
3, 8, 13, 18, 23
Do you notice a special pattern? It is obvious that each number after the first is five more than the preceding term. Meaning, the common difference of the sequence is five. Usually, the formula for the nth term of an arithmetic sequence whose first term is a1 and whose common difference is d is displayed below.
an = a1 + (n - 1) d
Steps in Finding the General Formula of Arithmetic and Geometric Sequences
1. Create a table with headings n and an where n denotes the set of consecutive positive integers, and an represents the term corresponding to the positive integers. You may pick only the first five terms of the sequence. For example, tabulate the series 5, 10, 15, 20, 25, . . .
n an
1
5
2
10
3
15
4
20
5
25
2. Solve the first common difference of a. Consider the solution as a tree diagram. There are two conditions for this step. This process applies only to sequences whose nature are either linear or quadratic.
Condition 1: If the first common difference is a constant, use the linear equation ax + b = 0 in finding the general term of the sequence.