Question

The sum of first n terms of an AP is given by Sn=3n^2-n. Find the AP

Answer 1

given sum of first n terms of a given terms:

Sn =3n2 - n

giving some values for n we get:

if n=1

s1 = 3*12 - 1

= 3-1

= 2

so we get the sum of 1 term = 2.in fact the first term = 2.

if n=2:

s2 = 3*22 - 2

= 3*4 - 2

= 12-2

= 10

so the sum of first two terms = 10.

so the second term = sum of two terms - the first term

= 10 - 2

= 8.

so d = 8-2

= 6

so the required AP is:

2,2+6,2+(2*6),2+(3*6)...

2,8,14,20,26,32...

a25 = a+19d

= 2 + 19*6

= 2 + 114

a25 = 116

Answer 2

Answer:

let n=1

S1= 3 - 1 = 2 =a1

Now let n=2

S2 = a1 + a2 = 3x4-2=10

10 = 2 + a2

a2 = 8

common difference= a2 - a1= 8 - 2= 6

so the AP will be :

2,8,14,20,26,32,38...