Question

What is the first term in an arithmetic sequence?

Answer 1

Arithmetic sequence:

• The arithmetic progression is a series of numbers in which the difference between any consecutive terms is equal.
• The first term of a series is the number with which the series begins.
• It is an important factor in determining the $n^{th}$term of the series and also the sum of the given series.
• The first term is generally represented as $"a"$.
• The formula to find the $n^{th}$ term of a series is $a_n=a+\left(n-1\right)d,$where $n$is the number of terms, $d$ is the common difference, $a_n$is the $n^{th}$ term and $a$is the first term.
• The formula for the sum of $n$terms in an arithmetic series is $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$ where $n$is the number of terms, $d$ is the common difference, and $a$is the first term.
• If the first and the $n^{th}$ term of the series are known, The sum is $S_n=\frac{n}{2}\left[a+a_n\right]$ where $n$ is the number of terms, $a$is the first term, $a_n$is the $n^{th}$ term.