Question

how are sequence and equation related? Explain your answer​

Answer 1

Relation between Sequence and Equation

Explanation:

• When several terms of a sequence are given, it is possible to find a general formula for the sequence by analyzing it's terms.
• This formula is generally represented in form of an equation. Assuming that there are $n$ terms in that sequence, the expression is generally calculated for the $n^{th}$ term. In this kind of formula we plug in different values of $n$ for example 1, 2 or 3 to calculate the first, second or third term respectively.
• $a_{n}=a+(n-1)d$ is one such formula for an arithmetic progression. Here $a_{n}$ stands for the $n^{th}$ term, $a$ stands for the first term of the sequence and $d$ stands for difference between any two consecutive terms, or we can say that number added to previous term to get the next term.
• Sequences can be generated by using other operations such as multiplication, division, exponent, logarithms etc. In that case the equations generated for each of them will be of a different format because the terms in those sequences would be related by different means.