Question

It is the question of A.P.

Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by-----
d=Sn-KSn-1+Sn-2, then K=?
(a)1 (b)2 (c)3 (d)none of these

Please give me answer with explanation

Answer 1

For d, let us take n=3
d=S₃-KS₃-₁+S₃-₂
d= a+2d - K(a+d) + a
d= a+2d -Ka-Kd+a
-2d+d - 2a = -k(a+d)
-d-2a = -k(a+d)
-2a-d = -k(a+d)
-1(2a+d)=-k(a+d)
2a+d = k(a+d)
2a+d / a+d = k
2 S₁ / S₁ = k
∴K = 2
option (b) is correct

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Yours, Jahnavi.

Answer 2

Answer:

Option (B) 2

Step-by-step explanation:

For d, let us take n=3

d=Sum₃-KSum₃-₁+Sum₃-₂

d= a+2d - K(a+d) + a

d= a+2d -Kd+a-Ka

-2d+d - 2a = -k(a+d)

-d-2a = -k(a+d)

-2a-d = -k(a+d)

-1(2a+d)=-k(a+d)

2a+d = k(a+d)

2a+d / a+d = k

2 Sum₁ / Sum₁ = k

∴K = 2