CBSE BOARD X, asked by saraamalik12300, 11 months ago

✨✔️♦️derivation of formula in Ap is important ???? according to exm point of u .... [CBSE class 10th ]
Q: if yes then please derive the formula

Answers

Answered by Jalay07
2

Answer:

I think derivation of AP has not been asked in any of the examinations.....

So.... Don't prepare AP derivation.... It won't come.... Most probably...

Thank you

Jalay

Answered by paroshnee18
1

Answer:

Explanation:

d = common difference

a1 = first term

a2 = second term

a3 = third term

am = mth term or any term before an

an = nth term or last term

 

d=a2−a1=a3−a2=a4−a3 and so on.

 

then,

Derivation for an in terms of a1 and d

a1=a1

a2=a1+d

a3=a2+d=(a1+d)+d=a1+2d

a4=a3+d=(a1+2d)+d=a1+3d  

a5=a4+d=(a1+3d)+d=a1+4d

...

am=a1+(m−1)d

...

an=a1+(n−1)d

 

similarly,

an=an

an−1=an−d

an−2=an−1−d=(an−d)−d=an−2d

an−3=an−2−d=(an−2d)−d=an−3d

an−4=an−3−d=(an−3d)−d=an−4d  

...

am=an−(n−m)d

...

a1=an−(n−1)d

 

Derivation for the Sum of Arithmetic Progression, S n

Sn=a1+a2+a3+a4+...+an

Sn=a1+(a1+d)+(a1+2d)+(a1+3d)+...+[a1+(n−1)d]   ←   Eq. (1)

Sn=an+an−1+an−2+an−3+...+a1  

Sn=an+(an−d)+(an−2d)+(an−3d)+...+[an−(n−1)d]   ←   Eq. (2)

 

Add Equations (1) and (2)

2Sn=(a1+an)+(a1+an)+(a1+an)+(a1+an)+...+(a1+an)

2Sn=n(a1+an)

Sn=n2(a1+an)

 

Substitute an = a1 + (n - 1)d to the above equation, we have

Sn=n/2{a1+[a1+(n−1)d]}

Sn=n/2[2a1+(n−1)d]

THIS IS NOT FOR EXAM POINT OF VIEW...

but i did it for helping

pls mrk as brainliest

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