Question

The sum of first n terms of an AP is 3n2-4n. Determine the AP and its 8th term. Also find its nth term.

Answer 1

Sn=3n²-4n

S₁= 3(1)²-4(1) = A₁

3 - 4= -1

a= -1

S₂=3(2)²-4(2)

=3 x 4 - 8

= 12-8 =4

so,on subtracting S₂ - S₁ , we get A₂

S₂-S₁

4 -(-1)= 4+1

=5 = A₂

So the common difference is A₂-A₁

= 5-(-1)

=6

so the 8th term of the AP will be

A₈= a+(n-1)d

= -1+(8-1)6

= -1+(7)6

=41

so the nth term of the AP will be

Aⁿ= a+(n-1)d

= -1 + (n-1)6

= -1-6+6n

= 6n-7