Question

How do you use a graphing calculator to find the sum of the arithmetic series $\sum {\left( {3n - 1} \right)}$ from $n = 10$ to $50$ ?

Answer 1

As we know the graphing calculator is used for solving simultaneous equations, plotting graphs etc and we can perform many other tasks using this calculator. Here, the given equation is of an Arithmetic series in which we need to find the summation of terms ranging 10 to 50 in which, here using the graphing calculator we need to find a step by step solution.

Complete step by step answer:
Graphing calculator is a tool used to find simultaneous equations, plotting graphs, finding sum of series etc. Here we need to find sum of arithmetic series for the term $\sum {\left( {3n - 1} \right)}$with the range $\sum\limits_{n = 10}^{50} {\left( {3n - 1} \right)}$.

First step: ON the calculator, here the calculator used is TI-84 Plus Silver Edition Graphical Display Calculator (GDC) to solve this sum.
Second step: To get the particular functions option, we need to press “Alpha Key” + “Window Key” in your calculator. After these various options are displayed such as FRAC, FUNC, MTRX, YVAR etc in which we need to find the function value.
Third step: Press on the FUNC option in which again various options are displayed as 1.abs, 2. $\sum {}$, 3. nDeriv, 4. fnInt etc. In this we need to find for summation $\sum {}$ , hence select option 2. After this we get the screen which displays$\sum\limits_{}^{} {\left( {} \right)}$ with blank squares at top and bottom of $\sum {}$ term as$\sum\limits_{n = a1}^{n = an} {\left( {sum} \right)}$.
Fourth step: As the summation term asks for values to enter, hence by entering the values it is displayed as $\sum\limits_{n = 10}^{50} {\left( {3n - 1} \right)}$.
Fifth step: To enter the n value use “Alpha Key” on the graphing calculator. Then press “ENTER KEY” to obtain the result of the sum.

Hence the result is displayed as $3649$.

Note: To obtain any functional values of the terms assigned such as arithmetic series, geometric series, derivatives etc and many other algebraic functions can be solved using graphing calculator in which we can find out the terms easily to solve any algebraic and simultaneous equations.