# How do you find the sum of an arithmetic sequence?

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## How do you find 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.

## What is the nth term rule for the sequence in number 3?

3(1),3(2),3(3)… so the nth term is simply 3 x n. In this sequence the difference is 3 , the nth term rule is 3n(where n = 1,2,3,…)

**What is the third term of a sequence that has a first term of 3 and a common ratio of 3?**

27

Answer: The third term of a geometric progression with first term 3 and common ratio 3 is 27.

### What is arithmetic sum?

The sum of the arithmetic sequence formula is defined as the formula to calculate the total of all the terms present in an arithmetic sequence. We know that an arithmetic series of finite arithmetic progress follows the addition of the members which is given by (a, a + d, a + 2d, …)

### What is sum of sequence?

The sum of the terms of a sequence is called a series . If a sequence is arithmetic or geometric there are formulas to find the sum of the first n terms, denoted Sn , without actually adding all of the terms.

**What is the sum of three odd numbers?**

In general, by taking any 3 odd numbers their sum will be odd. Hence, the sum of three odd numbers is odd.

#### What is the rule for finding the nth term in number 1?

Finding the nth Term of an Arithmetic Sequence Given an arithmetic sequence with the first term a1 and the common difference d , the nth (or general) term is given by an=a1+(n−1)d .

#### What is the third term of a sequence that has a first term of 3?

Answer: The third term of a geometric progression with first term 3 and common ratio 3 is 27.

**What is the third term in a sequence?**

The three dots mean to continue forward in the pattern established. Each number in the sequence is called a term. In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on. The notation a 1, a 2, a 3,… a n is used to denote the different terms in a sequence.