Question

The sum of first n terms of an arithmetic sequence is 3n²+4n write the algebraic from of the sequence​

Answer 1

EXPLANATION.

• GIVEN

sum of n terms of an Ap = 3n^2 + 4n

write the algebraic form of the sequence.

Let,

$\large\bold{t_{n} \: = s_{n} \: - \: s_{n - 1}}$

Tn = 3n^2 + 4n - [ 3( n - 1)^2 + 4( n - 1 )]

3n^2 + 4n - [ 3 ( n^2 + 1 - 2n ) + 4n - 4 ]

3n^2 + 4n - [ 3n^2 + 3 - 6n + 4n - 4 ]

3n^2 + 4n - 3n^2 - 3 + 6n - 4n + 4

6n + 1

Therefore,

algebraic form of an Ap = 6n + 1

More information,

Formula of n terms of an Ap

$\bold{a_{n} \: = a \: + (n - 1)d}$

sum of n terms of an Ap

$\bold{s_{n} \: = \frac{n}{2} (2a + (n - 1)d)}$