Question

What is the use of Arithmetic Progression in daily life?

Answer 1

To know what is the use of Arithmetic progression in daily life, we should first know what Arithmetic progression is. Arithmetic progression or AP is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value.

Formula used:
We can solve A,P with the formula for finding the ${n^{th}}$ term of an AP , i.e.
${a_n} = a + (n - 1)d$,
Where we know that $a$ is the first term, $d$ is the common difference and $n =$number of terms.

Complete step by step answer:
We can say that arithmetic progression can be applied in real life by analysing a certain pattern that we see in our daily life. Let us take an example of a natural geyser that produces long eruptions that are easily predictable and no one controls it. Let us say that the time of eruptions is based on the length of the previous eruption.

If an eruption lasts $1$ minute, then the next eruption will occur approximately in $46$ minutes. Again if an eruption lasts $2$ minute, then the next eruption will occur approximately in $58$ minutes. Then we say that the eruptions thus occur in the sequence of $46,58,70,82,94,...$ with a common difference of $12$.
We can say that the number of month that we see in daily life is also in A.P, i.e.
$1,2,3,4,5,6...,12$
Here we have first term
$a = 1$
Common difference is
$d = 2 - 1 = 1$
And we have the last term here i.e.
$n = 12$
We can take another example when we are waiting for a bus. We will assume that the traffic is moving at a constant speed, so we can predict when the next bus will come.

Note: We should note that we can find the sum of the ${n^{th}}$ term of AP by the formula: ${S_n} = \dfrac{n}{2}\left[ {2a + \left( {n - 1} \right)d} \right]$ . We should know that if we have to find the sum of a finite arithmetic progression, when its first and last term are known, then the formula is ${S_n} = \dfrac{n}{2}(a + l)$ where, $a$ is the first term and $l$ is the last term of the A.P .