Question

sum of first n terms of AP is given by Sn=(3n) (3n)-n;Determine AP and its 12th term
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Answer 1

The sum of first n term is

The sum of first n - 1 term is

The difference of sum of (n – 1) and n will give us the value of

The value of

Putting the value of n = 1, 2 to determine the first value of the series and the common difference

Now to find the 12th term of series we use the formula of Arithmetic Progression:

Therefore, the value of twelfth term of series is 65, whereas the value of nth term of series is 6n-7.

Answer 2

Answer:

let n=1,

then Sn=3n(3n)-n

S1=3(1)(3)(1)-1

=3(3)-1

=9-1

8

let n=2

s

S2=3(2)(3)(2)-2

=36-2

=34

A1=8

A2=34-8

A2=26

d=18

A12=a+11d

8+11(18)

8+198

206