Question

the sum of the first n terms of an AP is 5n-n2 find the nth term of this AP

Answer 1

Let Sn denotes the sum of first n terms of the AP.

Answer 2

Answer:

Sn = 5n - n²

° S1 = 5 × 1 - ( 1 )²

S1 = 5 - 1

S1 = 4

• a1 = S1

a1 = 4

° S2 = 5 × 2 - ( 2 )²

S2 = 10 - 4

S2 = 6

• a2 = S2 - S1

a2 = 6 - 4

a2 = 2

d ( common difference ) = a2 - a1

d = 2 - 4 = - 2

To find nth term ,

an = a + ( n - 1 )d

an = 4 + ( n - 1 ) ( - 2 )

an = 4 - 2n + 2

an = 6 - 2n