Question

How do I find the sum of an arithmetic sequence on a calculator?

Answer 1

Hint: An arithmetic sequence is a sequence in which all the numbers in the sequence are in a definite pattern. In an arithmetic sequence if we consider two consecutive numbers then the difference between them is a constant which can also be called a common difference. The sum of an arithmetic sequence can be given by
\[{{s}_{n}}=\dfrac{n}{2}\left( 2a+\left( n-1 \right)d \right)\]

Complete step by step answer:
In the above expression, \[{{s}_{n}}\] is called the sum of n terms, n is a number of terms, a is the first term of the sequence and d is a common difference.
If we know the number of terms, the first term of the sequence, and the common difference of the sequence we can find the sum of an arithmetic sequence on a calculator.
First, “ON” the calculator and then substitute the values according to the formula of the sum of an arithmetic sequence and press the button “ANS” to get the solution.
If we know the last term of the sequence then we can easily calculate the sum of an arithmetic sequence by using the given formulae.
\[{{s}_{n}}=\dfrac{n}{2}\left( a+{{a}_{n}} \right)\]
Where \[{{a}_{n}}\] is the last term of the sequence.
Therefore, In this way, we can find the sum of an arithmetic sequence on a calculator.

Note:
While solving questions from arithmetic sequence one common error would be not correctly finding the value of d, the common difference. Sometimes sequences of fractions are confusing. You might check that the d calculated is consistently true for any two successive terms of the sequence. This helps to verify the sequence. We can also find the sum by applying \[\sum\limits_{k=1}^{n}{\left( dk+b \right)}\] where d is a common difference, b is the addition of the first term, and -d and k vary from 1 to the number of terms.