Question

How do I find the ${{n}^{th}}$ partial 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 fixed order. The sum of an arithmetic sequence is given by ${{S}_{n}}=\dfrac{n}{2}\left( 2a+\left( n-1 \right)d \right)$. To find the ${{n}^{th}}$ partial sum of an arithmetic sequence on a calculator we need to follow some steps.

Complete step by step solution:
We have to write the steps involved in finding the ${{n}^{th}}$ partial sum of an arithmetic sequence on a calculator.
We know that to find the ${{n}^{th}}$ partial sum of an arithmetic sequence formula is given as ${{S}_{n}}=\dfrac{n}{2}\left( 2a+\left( n-1 \right)d \right)$
Here, n = total number of terms
a = first term of the sequence
d = common difference between the terms
When we have all values we just need to substitute the values in the above formula.
We can solve the obtained equation by calculator by entering the values and solving operations one by one. Scientific calculators allow us to enter an equation then by pressing the ANS button we get the sum of the sequence.

Note: As there is no special button to find the value of ${{n}^{th}}$ partial sum of an arithmetic sequence. As the formula contains simple arithmetic operations so we can easily solve the equation by using the calculator. The common mistake is made by students in identifying the sequence. First check the sequence by finding the common difference between the terms. The common difference between two terms remains the same for the sequence.