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- Arithmetic Sequences Calculator

This online tool can help you find $n^{th}$ term and the sum of the first $n$ terms of an arithmetic progression. Also, this calculator can be used to solve much more complicated problems. For example, the calculator can find the common difference ($d$) if $a_5 = 19 $ and $S_7 = 105$. The biggest advantage of this calculator is that it will generate all the work with detailed explanation.

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examples

example 1:ex 1:

$1 + 2 + 3 + 4 + . . . + 98 + 99 + 100 = ? $

example 2:ex 2:

The first term of an arithmetic sequence is equal to $\frac{5}{2}$ and the common difference is equal to 2.
Find the value of the 20^{th} term.

example 3:ex 3:

An arithmetic sequence has a common difference equal to $7$ and its 8^{th} term is equal to $43$. Find its first term.

example 4:ex 4:

Determine the first term and difference of an arithmetic progression if $a_3 = 12$ and the sum of first 6 terms is equal 42.

example 5:ex 5:

The first term of an arithmetic progression is $-12$, and the common difference is $3$
determine how many terms must be added together to give a sum of $1104$.

**Definition:**

Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant. The constant is called the common difference ($d$).

**Formulas:**

The formula for finding $n^{th}$ term of an arithmetic progression is $\color{blue}{a_n = a_1 + (n-1) d}$, where $\color{blue}{a_1}$ is the first term and $\color{blue}{d}$ is the common difference.

The formulas for the sum of first $n$ numbers are $\color{blue}{S_n = \frac{n}{2} \left( 2a_1 + (n-1)d \right)}$ and $\color{blue}{S_n = \frac{n}{2} \left(a_1 + a_n \right)}$.

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