# How do you find the first three terms of the arithmetic series n=19, #a_n=103#, #S_n=1102#?

##### 3 Answers

See explanation.

#### Explanation:

First we have to write everything which is given and what we are looking for:

Given:

To calculate:

First we can use the sum formula to calculate

#S_19=(a_1+a_19)/2*19#

#1102=(a_1+103)/2*19#

#2204=(a_1+103)*19#

#a_1+103=116#

#a_1=13#

Now we can calculate the common difference using two given terms:

#a_1+18*d=a_19#

#13+18*d=103#

#18*d=90#

#d=5#

Now having

**Answer:**

**The first three terms are: #13,18# and #23#.**

#### Explanation:

Here,

We know that,

*Arithmetic series* is

and **sum of first n-terms**

Now,

So,

Let,

From

From

Hence, first three terms of Arithmetic series are :

**The first three terms: **

#### Explanation:

**Total number of terms: **

**19th term: **

**Sum of the first 19 terms: **

In an **Arithmetic Sequence, ** the difference between one term and the next is a **Common Difference**:

The terms are:

**First Term** and **Common Difference**.

The **Sum of an arithmetic sequence** is called an **Arithmetic Series**.

**Sum to ****terms** of an arithmetic series:

**Find the **

Since,

Multiply both sides of the equation by

Flipping sides:

Subtract

Divide both sides by

Use **Common Difference**

When

Flipping sides:

Subtract

Divide by

Terms:

So,