Question

If Sr denotes the sum of the first r terms of an A.P. Then, S₃n: (S₂n — Sn) is
A. n
B. 3n
C. 3
D. none of these

Answer 1

answer : option (C) 3

Sr denotes the sum of the first r terms of an A.P.

let a is the first term and d is the common difference of the AP.

then, we know, Sn = n/2 [ 2a + (n - 1)d ]

S_(3n) = 3n/2 [2a + (3n - 1)d]

S_(2n) = 2n/2[2a + (2n - 1)d ]

now, S_(3n) : {S_(2n) - S_n}

= {3n/2[2a + (3n - 1)d]}/{2n/2[2a + (2n - 1)d] - n/2[2a + (n - 1)d]}

= {3n/2[2a + (3n - 1)d]}/{n/2[4a + (4n - 2)d - 2a - (n - 1)d ]}

= {3n/2[2a + (3n - 1)d]}/{n/2[2a + (4n - 2 - n - 1)d]}

= {3n/2[2a + (3n - 1)d]}/{n/2[2a + (3n - 1)d]}

= 3

hence option (C) is correct choice.

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