Question

the 1st and 2 nd term of an AP are a-b and b-a respectively.then d=​

Answer 1

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the 1st and 2 nd term of an AP are a-b and b-a respectively.then d=

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Given :first term(a)=a-b

second term (A2)=b-a

D(common difference)

$\bold{\boxed{D=first \:term(a) -second term(A2)}}$

$= > d = b - a - (a - b)$

$= b - a - a + b = b - 2a + b$

$= 2b - 2a = 2(b - a)$

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Formula for finding 'nth' term

$\bold{\boxed{an = a + (n - 1)d}}$

Formula for sum :

$\bold{\boxed{sn = \frac{n}{2} (2a + (n - 1)d)}}$

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Answer 2

Answer:

Given :first term(a)=a-b

second term (A2)=b-a

D(common difference)

\bold{\boxed{D=first \:term(a) -second term(A2)}}

D=firstterm(a)−secondterm(A2)

= > d = b - a - (a - b)=>d=b−a−(a−b)

= b - a - a + b = b - 2a + b=b−a−a+b=b−2a+b

= 2b - 2a = 2(b - a)=2b−2a=2(b−a)

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Formula for finding 'nth' term

\bold{\boxed{an = a + (n - 1)d}}

an=a+(n−1)d

Formula for sum :

\bold{\boxed{sn = \frac{n}{2} (2a + (n - 1)d)}}

sn=

2

n

(2a+(n−1)d)

Step-by-step explanation:

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