Question

the sum of first n terms of an AP is 3xsuare -2x ,find AP​

Answer 1

Question:

If the sum of first n terms of an AP is

3n^2 - 2n , then find the AP.

Note:(1)

In an A.P. ,the nth term is given by ;

T(n) = S(n) - S(n-1)

Also,

The common difference is given by;

d = T(n) - T(n-1)

Note:(2)

The nth term of an AP is also given by;

T(n) = a + (n-1)d , where a is the first term and d is the common difference.

Also,

To form any sequence , we require at least three terms.

Here,

S(n) = 3n^2 - 2n

Thus ,

S(n-1) = 3(n-1)^2 - 2(n-1)

= 3(n^2 - 2n + 1) - 2(n-1)

= 3n^2 - 6n + 3 - 2n + 2

= 3n^2 - 8n + 5

Hence,

=> T(n) = S(n) - S(n-1)

=> T(n) = (3n^2 - 2n) - (3n^2 - 8n + 5)

=> T(n) = 3n^2 - 2n - 3n^2 + 8n - 5

=> T(n) = 6n - 5

Now;

1st term of the AP = T(1)

= 6•1 - 5

= 6 - 5

= 1

2nd term of the AP = T(2)

= 6•2 - 5

= 12 - 5

= 7

1st term of the AP = T(3)

= 6•3 - 5

= 18 - 5

= 13

Hence, the required AP is ;

1 , 7 , 13 .......