Question

How to practice for Arithmetic Progression ( class 10)???

please give all important formula and concept

any one expert in AP here....

Answer 1

here is your answer OK ☺☺☺☺☺☺☺

If an eruption lasts for 2 minutes then the next eruption will occur in 58 minutes.
The eruptions thus occur in the sequence of 46, 58, 70, 82, 94..... with a common difference of 12. This pattern will come in handy the next time you visit yellowstone national park.

just like ☺☺☺

Another example is when you are waiting for a bus. Assuming that the traffic is moving at a constant speed you can predict the when the next bus will come.

If you ride a taxi, this also has an arithmetic sequence. Once you ride a taxi you will be charge an initial rate and then a per mile or per kilometer charge. This show and arithmetic sequence that for every kilometer you will be charge a certain constant rate plus the initial rate.

Arithmetic sequence can be applied in almost all aspects of our lives. We just have to analyze how it can be used in our day-to-day life. Having knowledge about this kind of sequence can give us a different perspective on how things happen in our lives..

main points ☺☺☺

nth Term of an AP
For a given AP, where a is the first term, d is the common difference, n is the number of terms in an AP and an be the last term, the relation is given as

an=a+(n−1)×d


From the formula of general term, we have:

an=a+(n−1).d

95=10+(n−1).5

(n−1)=17

n=18

Sum of First Terms of an AP:
Consider an AP consisting n terms.

First Term = a

Common Difference = d

nth term = an

Sum of n term is given as S=n2[2a+(n−1).d]

Proof:

Consider an AP : a, a+d, a+2d, …………., a+(n-1).d

Sum of first n terms = a + (a+d) + (a+2d) + ………. + [a+ (n-1).d] ——————-(i)
Writing the terms in reverse order, we have: S = [a+(n-1).d] + [a+(n-2).d] + [a+(n-3).d] + ……. (a) ———–(ii)

Adding both the equations term wise, we have

2S = [2a + (n-1).d] + [2a + (n-1).d] + [2a + (n-1).d] + …………. + [2a + (n-1).d] (n-terms)

2S = n. [2a + (n-1).d]

S=n2[2a+(n−1).d]

Answer 2

$<b> HOLA BUDDY HERE'S UR ANSWER$

$<b><huge>IMPORTANT TOPICS$

1. In arithmetic progression, the main topics to deal with are

⏺sequence and series..

the formula related to this are ,,

A(n)= a+ (n-1)d

then for the any sequence the three terms are common,,

a-d,a,a+d,,,,,

and the formula of any given term is

for ex : A8= a+7d ,,,
etc..

sum of n terms is given by,,

S(n)= n/2(2a+(n-1)d)

..

these formula can be changed according to the question,,,,

it can be also written as,,,

S(n)= n/2(A(n)+a)

$<marquee>hope helps u❤❤$