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

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation:

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: