the sum of n terms of an AP is 3n2-n find out the first term and the common difference - Maths - Arithmetic Progressions

Question

the sum of n terms of an AP is 3n2-n find out the first
term and the common difference

Priyanka Kedia · Accepted Answer

Dear Student,

Please find below the solution to the asked query :

$S_{n} = 3 n^{2} - n$

So, the first term

$a_{1} = S_{1} = 3 - 1 = 2$

$S_{2} = (3 \times 2^{2}) - 2 S_{2} = 12 - 2 S_{2} = 10$

The second term

$a_{2} = S_{2} - S_{1} = 10 - 2 = 8$

The common difference d = $a_{2} - a_{1} = 8 - 2 = 6$

Therefore, the first term is 2 and the common difference is 6.

Hope this would have clear your doubt. Do let us know in case of any further concerns.

Regards

the sum of n terms of an AP is 3n2-n. find out the first term and the common difference.