FutureStarr

A Sn Calculator

# Sn 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.

### Calculator

Arithmetic progression calculator work with steps shows the complete step-by-step calculation for finding the `n^{th}` term and the `n^{th}` partial sum of an arithmetic progression such that there is `5` terms in the arithmetic progression, the first term is `5`, and the common difference is `4`. For any other combinations the number of terms, the first term, and the common difference, just supply the other numbers as inputs and click on the on the "GENERATE WORK" button. The grade school students may use this arithmetic progression calculator to generate the work, verify the results or do their homework problems efficiently.

These terms in the geometric sequence calculator are all known to us already, except the last 2, about which we will talk in the following sections. If you ignore the summation components of the geometric sequence calculator, you only need to introduce any 3 of the 4 values to obtain the 4th element. The sums are automatically calculated from these values; but seriously, don't worry about it too much, we will explain what they mean and how to use them in the next sections. (Source: www.omnicalculator.com)

### Use

Now let's see what is a geometric sequence in layperson terms. A geometric sequence is a collection of specific numbers that are related by the common ratio we have mentioned before. This common ratio is one of the defining features of a given sequence, together with the initial term of a sequence. We will see later how these two numbers are at the basis of the geometric sequence definition and depending on how they are used, one can obtain the explicit formula for a geometric sequence or the equivalent recursive formula for the geometric sequence.

There is another way to show the same information using another type of formula: the recursive formula for a geometric sequence. It is made of two parts that convey different information from the geometric sequence definition. The first part explains how to get from any member of the sequence to any other member using the ratio. This meaning alone is not enough to construct a geometric sequence from scratch, since we do not know the starting point. This is the second part of the formula, the initial term (or any other term for that matter). Let's see how this recursive formula looks: (Source: www.omnicalculator.com)

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