Question

in an A.P the sum of n terms is given by Sn=n2-3n find the 30th term

Answer 1

Answer: 420

Step-by-step explanation:

$S_n=\frac{n}{2} (a+a_n)$

Also, $S_n=n^{2} -3n$

The sum of the first term is obviously the first term.

$S_n=n^{2} -3n\\S_1=1-3=-2\\S_2=4-6=-2$

$S_2 -S_1 =a_2\\-2+2=a_2\\a_2=0$

$d=a_{2}-a_{1}\\d=0-(-2)\\d=2$

a=-2

d=2

$S_{n}=\frac{n}{2} [2a+(n-1)d]\\S_{30}=15*(-4+29*2)\\S_{30}=15*54 = 810$

Answer 2

Answer:

Sn=n^2-3n

n=1

S1=-2

S1=a1

n=2

S2=-2

a2=S2-S1

-2-(-2)

-2+2

=0

d=a2-a1

0-(-2)

0+2=2

a30 =a+29d

=-2+29*2

=-2+58

=56