Question

The sum of the nth term of an ap is 5n square - 3n. Find the ap and also its 10th term

Answer 1

Hi.....!

Sn=5n²-3n.     (GIVEN)

So substitutng 1 in the place of n.

S₁=5(1)²-3(1)

S₁=5-3

We get,  S₁=2.

We know that sum of the first term will be the first term itself.

So, S₁=a₁=2.

Again, substituting 2 in the place of n,

we get    

S₂=5(2)²-3(2)

S₂=20-6

S₂=14.

We know that An=Sn-S(n-1)

so, a₂=S₂-S₁

        =14-2

   a₂=12.

Now we have got the first and the second term so we can find the common difference.

a₂-a₁=d

12-2=1o

.: d=10.

The a.p is 2, 12, 22, 32......

10th term=a+(n-1)d

               =2+(9)10

              =2+90

.:The tenth term is 92.

HOPE IT HELPED...!