Question

If sn the sum of first n terms of an ap is given by sn- 4n-n2 then find its nth terms and the common difference

Answer 1

S1 = sum of one term = first term = 4*1 - 1^2

= 4 - 1

= 3

t1 = 3

S2 = sum of first two terms = t1 + t2 = 4*2 - 2^2

= 8 - 4

= 4

t2 = 4 - t1 = 4 - 3 = 1

so first term of AP = a = 4

cd = t2 - t1 = 1 - 4 = -3

nth term = tn = a + (n - 1) d

= 4 + (n - 1) (-3)

= 4 - 3n + 3

= 7 - 3n