Question

what is the formula for the arithmetic sequence of the sum of the same sequence is given by sn=2n+3n2​

Answer 1

Answer:

6n-1

Step-by-step explanation:

sn= 3n^2+2n

so an= sn-s(n-1)

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

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

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

= 6n-1

Answer 2

Given:

Sum of same sequence $=2n+3n^{2}$

To find:

Formula for Arithmetic sequence.

Solution:

We know the relation between sum of $n$ terms and value of $n^{th}$ terms is given by

$a_{n}=S_{n}- S_{n-1}$

We have $S_{n}=2n+3n^{2}$

$a_{n}=2n+3n^{2} -(2(n-1)+3(n-1)^{2} )$

$a_{n}=2n+3n^{2} -(2n-2+3(n^{2} -2n+1))$

$a_{n}=2n+3n^{2} -(2n-2+3n^{2}-6n+3 )$

$a_{n}=2n+3n^{2} -(3n^{2}-4n+1 )$

$a_{n}=2n+3n^{2} -3n^{2} +4n-1$

$a_{n}=6n-1$

Final answer:

Hence, the sequence of the arithmetic progression is given by 6n -1.