Question

In an ap sn=n/2(7n-1) then the common difference is
a)3
b)5
c)7
d)9​

Answer 1

Answer:

a is the correct awnser ok

Answer 2

Given : Sₙ  = (n/2)(7n - 1)

To Find :   the common difference  

Solution:

Sₙ  = (n/2)(7n - 1)

n = 1

=> S₁  = (1/2)(7(1) - 1 )  =  3

S₁  =  a₁  = 3

S₂  = a₁ + a₂

S₂ =  (2/2)(7(2) - 1 )  =  13

a₁ + a₂ = 13

=> 3 + a₂ = 13

=> a₂ = 10

d = a₂ - a₁  = 10 - 3  = 7

Generalized method :

aₙ  = Sₙ - Sₙ₋₁

=> aₙ  =  (n/2)(7n - 1)   -  ((n-1)/2)(7(n-1) - 1)

=> aₙ  =  (n/2)(7n - 1)   -  ((n-1)/2)(7n - 8)

=> aₙ  = (1/2) (7n²  - n  - 7n² +15n - 8)

=>  aₙ  = (1/2) (14n - 8)

=> aₙ  = 7n - 4

d = aₙ - aₙ₋₁   = 7n - 4 - (7(n-1) - 4)  =  7

Hence common difference is 7

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