Question

If the sum of n terms of an ap is given by sn = a +bn + cn^2 where a, b, c are independent of n then n, then its common difference is

Answer 1

Answer:

d = 2c

Step-by-step explanation:

a1 = s1 = a + b + c

s2 = a + 2b + 4c

a2 = s2 - s1 = a + 2b +4c - a - b - c

a2 = b + 3c

s3 = a + 9b + 27c

a3 = s3 - s2 = a + 3b + 9c - a - 2b - 4c

a3 = b + 5c

AP : a + b + c, b + 3c, b + 5c

b + 3c - a -b -c = b + 5c - b - 3c

- a + 2c = 2c

a = 0

therefore, d = 2c