An arithmetic series contains n terms. show that if t1 = a−b and tn = a+b then the value of sn is independent of b.

[arithmetic sequences]

Sn is independent of b

Step-by-step explanation:

t1=a-b

tn=a+b

we know that nth term of arithmetic series is  an=a1+(n-1)d

so

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

⇒2b=(n-1)d-----------equation 1

formula for sum of n terms of arithmetic series

  Sn=(2a1+(n-1)d)

   ⇒Sn=(2(a-b)+2b)      (since (n-1)d=2b  from equation 1)

   ⇒Sn=(2a)  

therefore we can see that Sn is independent of b

we need the options

step-by-step explanation:

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