Question

hlo frnds [tex]
\: the \: sum \: of \: \\ frst \: n \: \: term \: of \: an \: ap \: is \: (3 {n}^{2} + 4 n). \: find \: \: its \: \\ n \: th \: term \: and \: its \: ap ?
​​

Answer 1

Solution :-

Sn = 3n² + 4n

Put, n = 1 ,2,3,4..........

#N=1

⟹ 3n² + 4n

⟹ 3(1)²+4

\ ⟹ 7

#put n = 2

⟹ 3(2)²+4(2)

⟹ =20

#put n = 3

\ ⟹ 3(3)²+4

⟹ = 31

S1 = 7

S2 = 20

S3 = 31

⟹ D = 6

⟹ A = 7

⟹ An = A + (n-1)D

= 7 + (n-1)6

An= 6n +1

putting n=1,2,3,4....

you will get its terms

A.P ----> 7,13,19......

Answer 2

Sn = 3n² + 4n

Put, n = 1 ,2,3,4..........

N=1

3n² + 4n

3(1)²+4

7

put n = 2

3(2)²+4(2)

=20

put n = 3

3(3)²+4

= 31

S1 = 7

S2 = 20

S3 = 31

D = 6

A = 7

An = A + (n-1)D

= 7 + (n-1)6

An= 6n +1

putting n=1,2,3,4....

you will get its terms

A.P ----> 7,13,19.